Maximum Likelihood Estimation Research Articles

Statistical methods to control for confounders in rare disease settings that use external control

ABSTRACT In the drug development for rare disease, the number of treated subjects in the clinical trial is often very small, whereas the number of external controls can be relatively large. There is no clear guidance on choosing an appropriate statistical method to control baseline confounding in this situation. To fill this gap, we conduct extensive simulations to evaluate the performance of commonly used matching and weighting methods as well as the more recently developed targeted maximum likelihood estimation (TMLE) and cardinality matching in small sample settings, mimicking the motivating data from a pediatric rare disease. Among the methods examined, the performance of coarsened exact matching (CEM) and TMLE are relatively robust under various model specifications. CEM is only feasible when the number of controls far exceeds the number of treated, whereas TMLE has better performance with less extreme treatment allocation ratios. Our simulations suggest bootstrap is useful for variance estimation in small samples after matching.

A New Statistical Approach Based on the Access of Electricity Application with Some Modified Control Charts

This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

Regression to the mean effect for bi-variate dispersed count data

Regression to the mean (RTM) occurs when extreme observations upon remeasurement are found closer to the population mean. Interventions are usually applied to subjects based on a cut-off point to check it effectiveness. The average difference of the pre-post observations called the total effect is the sum of RTM and intervention effects and needs to be accounted for RTM to avoid incorrect conclusions and unbiasedly estimate the intervention effect. The existing methods assume equidispersion and strict positive correlation for bivariate count data. This study considers a bivariate Poisson distribution which takes both the dispersion and negative correlation into consideration. Expressions for the total effect are derived and partitioned into RTM and intervention effects. The maximum likelihood estimators of the RTM and intervention effects are found numerically, and their asymptotic properties are verified via simulations. Data on the English premier league are used to estimate the RTM and intervention effects.

Estimating genomic relationships of metafounders across and within breeds using maximum likelihood, pseudo-expectation–maximization maximum likelihood and increase of relationships

BackgroundThe theory of “metafounders” proposes a unified framework for relationships across base populations within breeds (e.g. unknown parent groups), and base populations across breeds (crosses) together with a sensible compatibility with genomic relationships. Considering metafounders might be advantageous in pedigree best linear unbiased prediction (BLUP) or single-step genomic BLUP. Existing methods to estimate relationships across metafounders Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document} are not well adapted to highly unbalanced data, genotyped individuals far from base populations, or many unknown parent groups (within breed per year of birth).MethodsWe derive likelihood methods to estimate Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document}. For a single metafounder, summary statistics of pedigree and genomic relationships allow deriving a cubic equation with the real root being the maximum likelihood (ML) estimate of Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document}. This equation is tested with Lacaune sheep data. For several metafounders, we split the first derivative of the complete likelihood in a term related to Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document}, and a second term related to Mendelian sampling variances. Approximating the first derivative by its first term results in a pseudo-EM algorithm that iteratively updates the estimate of Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document} by the corresponding block of the H-matrix. The method extends to complex situations with groups defined by year of birth, modelling the increase of Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document} using estimates of the rate of increase of inbreeding (ΔF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta F$$\\end{document}), resulting in an expanded Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document} and in a pseudo-EM+ΔF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta F$$\\end{document} algorithm. We compare these methods with the generalized least squares (GLS) method using simulated data: complex crosses of two breeds in equal or unsymmetrical proportions; and in two breeds, with 10 groups per year of birth within breed. We simulate genotyping in all generations or in the last ones.ResultsFor a single metafounder, the ML estimates of the Lacaune data corresponded to the maximum. For simulated data, when genotypes were spread across all generations, both GLS and pseudo-EM(+ΔF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta F$$\\end{document}) methods were accurate. With genotypes only available in the most recent generations, the GLS method was biased, whereas the pseudo-EM(+ΔF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta F$$\\end{document}) approach yielded more accurate and unbiased estimates.ConclusionsWe derived ML, pseudo-EM and pseudo-EM+ΔF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta F$$\\end{document} methods to estimate Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\Gamma}}$$\\end{document} in many realistic settings. Estimates are accurate in real and simulated data and have a low computational cost.

On tracking varying bounds when forecasting bounded time series

We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded random variable. We introduce an extended log-likelihood estimation and design algorithms to track the bound through online maximum likelihood estimation. Since the resulting optimization problem is not convex, we make use of recent theoretical results on stochastic quasiconvex optimization, to eventually derive an Online Normalized Gradient Descent algorithm. We illustrate and discuss the workings of our approach based on both simulation studies and a real-world wind power forecasting problem.

Statistical Analysis of the Inverse Power Zeghdoudi Model: Estimation, Simulation and Modeling to Engineering and Environmental Data

Abstract In this research, we investigate a brand-new two-parameter distribution as an extension of the
power Zeghdoudi distribution (PZD). Using the inverse transformation technique on the PZD, the
produced distribution is called the inverted PZD (IPZD). Its usefulness in producing symmetric and
asymmetric probability density functions makes it the perfect choice for lifetime phenomenon mod-
eling. It is also appropriate for a range of real data since the relevant hazard rate function has one of
the following shapes: increasing, decreasing, reverse j-shape or upside-down shape. Mode, quantiles,
moments, geometric mean, inverse moments, incomplete moments, distribution of order statistics,
Lorenz, Bonferroni, and Zenga curves are a few of the significant characteristics and aspects explored
in our study along with some graphical representations. Twelve effective estimating techniques are
used to determine the distribution parameters of the IPZD. These include the Kolmogorov, least
squares (LS), a maximum product of spacing, Anderson-Darling (AD), maximum likelihood, mini-
mum absolute spacing distance, right-tail AD, minimum absolute spacing-log distance, weighted LS,
left-tailed AD, Cram ́er-von Mises, AD left-tail second-order. A Monte Carlo simulation is used to
examine the effectiveness of the obtained estimates. The visual representation and numerical results
show that the maximum likelihood estimation strategy regularly beats the other methods in terms of
accuracy when estimating the relevant parameters. The usefulness of the recommended distribution
for modelling data is illustrated and displayed visually using two real data sets and comparisons with
other distributions.

Abstract PS16-02: Efficacy and safety of first-line atezolizumab + bevacizumab + paclitaxel in patients with advanced triple-negative breast cancer: the ATRACTIB phase 2 trial

Abstract BACKGROUND Triple-negative breast cancer (TNBC) is an aggressive tumor characterized by poor outcomes and new treatment strategies are urgently required. The programmed cell death-ligand 1 (PD-L1) antibody (Ab) atezolizumab (ATZ) combined with first-line (1L) nab-paclitaxel (nab-PTX) is approved in multiple countries for the treatment of PD-L1-positive patients (pts) with advanced TNBC (aTNBC) based on a significant improvement in progression-free survival (PFS) and a numerically higher and clinically meaningful median overall survival (OS). A synergism between antiangiogenic therapy and immunotherapy (IO)-based strategies has been observed preclinically and in different tumor types, but data in aTNBC is lacking. METHODS ATRACTIB (NCT04408118) is an international, open-label, single-arm, phase 2 trial evaluating the efficacy and safety of 1L ATZ + BVZ + PTX for pts with aTNBC, regardless of their tumors’ PD-L1 status. Adult pts with untreated, unresectable locally advanced/metastatic TNBC were included. Pts who had received (neo)adjuvant taxane-based chemotherapy (CT) and/or IO and/or an antiangiogenic agent had to have had a relapse with a disease-free interval beyond 12 months (mo). Pts received intravenous ATZ 840 mg + BVZ 10 mg/kg on days (D)1 and D15 + PTX 90 mg/m2 on D1, 8, and 15 of every 28-day cycle until disease progression, intolerable toxicity, death, or patient withdrawal. Tumor assessments were performed every 8 weeks for the first 12 mo and every 12 weeks thereafter. Baseline PD-L1 expression was centrally assessed using 22C3 (combined positive score [CPS]) and SP142 (expression on tumor-infiltrating immune cells [ICs]) Abs. The primary endpoint was investigator-assessed PFS by RECIST v.1.1. Key secondary endpoints included OS, objective response rate (ORR), clinical benefit rate (CBR), duration of response (DoR), and safety. Median PFS was analyzed with exponential maximum likelihood estimation (H0: ≤7.0 mo; HA: ≥9.5 mo). We estimated that enrolling 100 pts would provide 80% power at one-sided α nominal level of 5%, assuming a 10% drop-out rate. RESULTS Between October 2020 and May 2022, 100 female pts from 28 centers across 5 European countries were included. Median age was 55.0 years (32.0 - 84.0), 57.0% of pts had visceral disease, 46.0% had ≥3 metastatic sites, and 70.0% had received prior treatment for early BC (taxane-based CT in 87.1% of them). A total of 82 and 85 tumor samples out of 100 pts were available for PD-L1 assessment using 22C3 and SP142 assays, respectively. Most pts had PD-L1-negative tumors (87.8% with 22C3 [CPS < 10] and 97.6% with SP142 [expression on < 1% positive of ICs]). At data cutoff (15th September 2023), 23 pts were still on therapy. With a median follow-up of 16.7 mo (1.1 - 34.1), median PFS was 11.0 mo (95% CI, 9.0 - 13.2). OS data were immature at data cutoff, with 30 events. Estimated 18-month OS was 69.4% (95% CI, 58.4% - 78.1%). ORR was 63.0% (95% CI, 52.8% - 72.4%), CBR was 79.0% (95% CI, 69.7% - 86.5%), and median DoR was 10.0 mo (95% CI, 7.2 - 13.8). Regarding safety, the most common treatment-emergent adverse events (TEAEs) were peripheral neuropathy (68.0%) and fatigue (62.0%). Grade (G) 3/4 treatment-related TEAEs occurred in 47.0% of pts, mainly peripheral neuropathy (13.0%) and neutropenia (12.0%). Any-grade immune-related TEAEs, thrombosis or embolism, and bleeding occurred in 13.0% (5.0%; G≥3), 4.0% (1.0%; G≥3), and 10.0% (0.0%; G≥3) of pts, respectively. There were no drug-related deaths. CONCLUSIONS 1L ATZ + BVZ + PTX demonstrated encouraging anti-tumor activity in aTNBC pts, most of them presenting with PD-L1-negative tumors. Median PFS seems to be much higher compared with that previously reported with other IO-based regimens in a similar patient population. The safety profile was consistent with the known safety data of ATZ and BVZ combined with CT, without significant added toxicity. These results merit further research of this combination for PD-L1-negative aTNBC. Citation Format: Maria Gion, Patricia Cortez-Castedo, Isabel Blancas, Alfonso Cortés, Frederik Marmé, Salvador Blanch, Serafin Morales Murillo, Nieves Díaz, Isabel Calvo-Plaza, Sabela Recalde, Alejandro Martínez-Bueno, Manuel Ruiz-Borrego, Elisenda Llabres, María Teresa Taberner, Michelino de Laurentiis, José Ángel García-Sáenz, Jana Repkova, Antonio Antón, Joseph Gligorov, Susana de la Cruz, Oliver Hoffmann, Jacques Medioni, Melissa Phillips, Miguel Sampayo-Cordero, Daniel Alcalá-López, José Manuel Pérez-García, Antonio Llombart-Cussac, Javier Cortés. Efficacy and safety of first-line atezolizumab + bevacizumab + paclitaxel in patients with advanced triple-negative breast cancer: the ATRACTIB phase 2 trial [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PS16-02.

Assessing the impact of non-tariff measures on Sri Lankan mango exports: insights, challenges, and recommendations

IntroductionWith the increase in non-tariff measures (NTMs) in recent years, understanding their impact on trade policies and agricultural exports is of utmost importance for countries like Sri Lanka, where the proliferation of NTMs has posed substantial impediments to its mango export industry. However, studying NTMs can be challenging due to their complex nature, diverse range, and limited information availability.MethodsThis research aims to investigate the significant effect of NTMs on Sri Lankan mango exports, identify the pivotal drivers influencing mango exports, and analyze the performance of mango exports in Sri Lanka. This study utilized a panel dataset of 16 importing countries spanning the period from 2000 to 2021. The primary focus was on examining NTM-related challenges and obstacles faced by the mango export industry in Sri Lanka. The identification and quantification of these obstacles were achieved through a multifaceted approach in which assessment of NTM-related rejections, both domestic and overseas, evaluation of NTM incidences using frequency and coverage ratio measures, and the deployment of various gravity model equations to quantify the effect of NTMs were taken into consideration. Probit, Ordinary Least Square, Random Effects, and Poisson Pseudo Maximum Likelihood estimation techniques were utilized for data analysis.ResultsThe findings indicate a significant inverse correlation between the increase in the total count of NTMs and Sri Lankan mango exports if the country aims to export more mangoes to relevant markets, while Sanitary and Phytosanitary Measures (SPS), Technical Barriers to Trade (TBT), and Pre-shipment Inspection (PSI) contributed to increased mango exports. Among other explanatory variables, the GDP of both importing and exporting countries had a positive influence on Sri Lankan mango exports. Surprisingly, the distance to the importing country had no significant effect, though it shows a negative sign.DiscussionThis study provides valuable insights into the impact of NTMs on Sri Lankan mango exports. It highlights the considerable influence of NTMs on the overall fresh fruit export sector. We recommend proactively aligning internal quality testing regulations with the standards required by destination countries to promote future expansion.

Non Pilot Data-Aided Carrier and Sampling Frequency Offsets Estimation in Fast Time-Varying Channel

This paper considers the non pilot data-aided estimation of the carrier frequency offset (CFO) and sample frequency offset (SFO) of orthogonal frequency division multiplexing (OFDM) signals in fast time-varying channel. The main obstacle is the time-variant channel response, which deteriorates the estimation validity. A practical approach to mitigate this impact is to reduce the time consumption of one-shot estimation. In this way, we propose a method to reduce the time consumption to within one OFDM symbol duration. The maximum likelihood (ML) estimator is derived based on the observations of frequency domain constellations output of two FFTs on one symbol; its closed-form approximation is then derived to reduce the calculation burden. Remarkably, our method does not require any training symbol or pilot tone embedded in the signal spectrum, therefore achieves the highest spectral efficiency. Theoretical analysis and simulation results are employed to assess the performance of proposed method in comparison with existing alternatives.

Powerless in the storm: Severe weather-driven power outages in New York State, 2017–2020

The vulnerability of the power grid to severe weather events is a critical issue as climate change is expected to increase extreme events, which can damage components of the power grid and/or lessen electrical power supply, resulting in power outages. However, largely due to an absence of granular spatiotemporal outage data, we lack a robust understanding of how severe weather-driven outages, their community impacts, and their durations distribute across space and socioeconomic vulnerability. Here, we pair hourly power outage data in electrical power operating localities (n = 1865) throughout NYS with urbanicity, CDC Social Vulnerability Index, and hourly weather (temperature, precipitation, wind speed, lightning strike, snowfall) data. We used these data to characterize the impact of extreme weather events on power outages from 2017–2020, while considering neighborhood vulnerability factors. Specifically, we assess (a) the lagged effect of severe weather on power outages, (b) common combinations of severe weather types contributing to outages, (c) the spatial distribution of the severe weather-driven outages, and (d) disparities in severe weather-driven outages by degree of community social vulnerability. We found that across NYS, 39.9% of all outages co-occurred with severe weather. However, certain regions, including eastern Queens, upper Manhattan and the Bronx of NYC, the Hudson Valley, and Adirondack regions were more burdened with severe weather-driven outages. Using targeted maximum likelihood estimation, we found that the frequency of heat-, precipitation-, and wind-driven outages disproportionately impacted vulnerable communities in NYC. When comparing durations of outages, we found that in rural regions, precipitation- and snow-driven outages lasted the longest in vulnerable communities. Under a shifting climate, anticipated increases in power outages will differentially burden communities due to regional heterogeneity in severe weather event severity, grid preparedness, and population socioeconomic profiles/vulnerabilities. As such, policymakers must consider these characteristics to inform equitable grid management and improvements.

Performance Analysis of Filtered OFDM using MLE for Wireless Communication Networks

Introduction: OFDM has evolved as an effective modulation format for 4G mobile network technologies, Long-Term Evolution, and Worldwide Interoperability for Microwave Access. OFDM is the modulation technique adopted for communication standards such as DSL, wireless LAN, DVB, and DAB. However, because CP-OFDM has considerable out-of-band emission that may interfere with transmissions in adjacent bands and applies a single set of parameters to the whole band to fulfill a given service, it is unable to accommodate the diversity of services. The objective of the research is to develop a novel waveform with better adaptability than CP-OFDM that employs filters to increase spectrum containment. In this view, an FIR filter that uses the Blackman window function to lessen the OOBE is proposed in this manuscript. Filtered OFDM is sensitive to carrier frequency offset (CFO). CFO increases the Inter-Carrier Interference (ICI) in F-OFDM systems. However, research work that combines the CFO compensation technique with filtered OFDM has not been listed in the literature so far. Methods: In this paper, Maximum likelihood estimation is used to cancel the ICI caused by the CFO. The high PAPR of filtered OFDM is one of its drawbacks. The amplitude clipping method is used to reduce the PAPR. The distortion caused by amplitude clipping is prevented by filters used in the FOFDM system. Highlights: • A novel waveform addressing OOBE issues in OFDM is developed for 4G wireless communication networks. • An innovative solution using MLE is proposed to address the challenges faced by the filtered OFDM system due to the CFO. • Article addresses the high PAPR problem of filtered OFDM. method: This work presents a FIR filter that uses the Blackman window function to lessen the OOBE. Filtered OFDM is sensitive to carrier frequency offset (CFO). CFO increases the inter-carrier interference in F-OFDM systems. However, research work is not listed in the literature so far that combines CFO compensation technique with filtered OFDM. In this paper Maximum likelihood estimation is used to cancel the ICI caused by CFO. The high PAPR of filtered OFDM is one of its drawbacks. The amplitude clipping method is used to reduce the PAPR. The distortion caused due to amplitude clipping is prevented by filters used in the F-OFDM system Result: The performance of filtered OFDM with amplitude clipping is analyzed in terms of BER, PSD, and PAPR over the AWGN channel. Conclusion: Simulation results show that, when compared to the traditional OFDM system, such a combined method effectively suppresses PAPR while maintaining good BER (Bit Error Rate) and OOBE performance.

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

This paper derives the bivariate version of the extended standard U-quadratic (eSU)  distribution using the method of compounding or pseudo family of distributions. The joint probability and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape with the following properties: $(i)$ $X$ and $Y$ have bathtub shapes; $(ii)$ $X$ has constant and $Y$ has bathtub shapes; and $(iii)$ $X$ has inverted bathtub and $Y$ has bathtub shapes. Moreover, some properties of the derived distribution such as the marginal distribution, conditional distributions, conditional moments, product and ratio moments are derived. Further, the maximum likelihood estimation is performed to estimate the parameters of the derived distribution. Also, a simulation study is carried out to evaluate the behavior of the estimates of the parameters. Moreover, we derive a new bivariate Kumaraswamy distribution and use it to simulate bivariate data with $X$ and $Y$ having bathtub shapes. Furthermore, A new bivariate version of the Cubic Transmuted Uniform (CTU) distribution is also derived. Finally, the proposed Bivariate eSU distribution is applied to simulated data and compared with the said Bivarite Cubic Transmuted Uniform distribution. The result shows that the proposed Bivariate eSU distribution provides a better fit for the said simulated dataset as compared with the Bivariate CTU distribution.

On efficiency of locally D-optimal designs under heteroscedasticity and non-Gaussianity

In the classical theory of locally optimal designs, which is developed within the framework of the center+error model, the most efficient design is the one based on MGLE, the maximum Gaussian likelihood estimator. However, practical scenarios often lack of complete information as to the governing probability model for the response measure and deviate from Gaussianity and homoscedasticity assumptions, in which, MqLE, the maximum quasi-likelihood estimator, has been advocated in the literature. In this work, we examine the locally optimal design based on the novel oracle-SLSE, the second-order least-square estimator, in the case where the underlying probability model is incompletely specified. We find that in a general setting, our oracle SLSE-based optimal design, incorporating skewness and kurtosis information, outperforms those based on MqLE or MGLE. Our numerical experiment supports this, with locally D-optimal designs based on MqLE approaching the efficiency of oracle-SLSE designs in some cases. This research guides the choice of estimators in practical scenarios departing from ideal assumptions.

Numerical Comparison by using Some Criteria to Estimate the Two Parameters of the Exponentiated Exponential Distribution

     The present paper shows a numerical comparison by using the number of the following criteria: mean squared, root mean Square, mean absolute, and relative mean squared error values between the methods, namely  maximum likelihood and Bayesian estimators for the two parameters of the exponentiated exponential distribution. In estimating the maximum likelihood, The equations cannot be solved directly, Then Newton-Raphson method is used. Because of Bayes estimators under scale invariant squared and weighted composite linear-exponential loss functions the ratios cannot be simplified in a closed form. So, we use Lindley approximation. MATLAB program is used to display the results.

A Spatiotemporal Probabilistic Graphical Model Based on Adaptive Expectation-Maximization Attention for Individual Trajectory Reconstruction Considering Incomplete Observations

Spatiotemporal information on individual trajectories in urban rail transit is important for operational strategy adjustment, personalized recommendation, and emergency command decision-making. However, due to the lack of journey observations, it is difficult to accurately infer unknown information from trajectories based only on AFC and AVL data. To address the problem, this paper proposes a spatiotemporal probabilistic graphical model based on adaptive expectation maximization attention (STPGM-AEMA) to achieve the reconstruction of individual trajectories. The approach consists of three steps: first, the potential train alternative set and the egress time alternative set of individuals are obtained through data mining and combinatorial enumeration. Then, global and local potential variables are introduced to construct a spatiotemporal probabilistic graphical model, provide the inference process for unknown events, and state information about individual trajectories. Further, considering the effect of missing data, an attention mechanism-enhanced expectation-maximization algorithm is proposed to achieve maximum likelihood estimation of individual trajectories. Finally, typical datasets of origin-destination pairs and actual individual trajectory tracking data are used to validate the effectiveness of the proposed method. The results show that the STPGM-AEMA method is more than 95% accurate in recovering missing information in the observed data, which is at least 15% more accurate than the traditional methods (i.e., PTAM-MLE and MPTAM-EM).

A new computational framework for log-concave density estimation

AbstractIn statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the log-concave maximum likelihood estimator, adoption of this method has been hampered by the complexities of the non-smooth convex optimization problem that underpins its computation. We provide enhanced understanding of the structural properties of this optimization problem, which motivates the proposal of new algorithms, based on both randomized and Nesterov smoothing, combined with an appropriate integral discretization of increasing accuracy. We prove that these methods enjoy, both with high probability and in expectation, a convergence rate of order 1/T up to logarithmic factors on the objective function scale, where T denotes the number of iterations. The benefits of our new computational framework are demonstrated on both synthetic and real data, and our implementation is available in a github repository (Log-Concave Computation).

APPLICATION OF GENERALIZED EXTREME VALUE DISTRIBUTION TO ANNUAL MAXIMUM RAINFALL

Generalized Extreme Value Distributions was used to model annual maximum rainfall data in Akure, Ondo State, Nigeria from 1981-2019. The parameters of the distribution are estimated using the maximum likelihood estimation method. The model fit indicated that the shape  parameter is negative this suggests that Fréchet distribution is the appropriate model for describing annual maximum rainfall in Ondo-state Nigeria. The estimated return levels for different return periods revealed an increase in the value over the years.

Data-Driven Algorithms for Two-Location Inventory Systems

In this paper, we consider a multiperiod, two-location inventory system with unknown demand distributions and perishable products. Products can be transshipped from the location with excess inventory to the other with excess demand to better fulfill customer demand. The demand distributions are assumed to follow a family of parametric distributions and can only be learned on the fly. To address the challenge, we propose a data-driven inventory management algorithm called DD2LI that achieves a good performance in terms of regret. This algorithm, DD2LI, employs maximum likelihood estimation to approximate the unknown parameter and determines the order quantity based on these estimations. In addition, we emphasize a key assumption that tightens regret bound. Finally, we test the effectiveness of our proposed algorithm by conducting numerical experiments for two scenarios.