Maximum Likelihood Estimation Research Articles

Likelihood-based inference for semi-parametric transformation cure models with interval censored data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

A New Family of Distributions Based on Amalgamation of Two Methods with an Application to the Rayleigh Model

In this paper, we present the Alpha power generalized odd generalized exponential-G (APGOGE-G) family of distributions and provides the most common shapes of the hazard rate function: increasing, decreasing, bathtub, and inverted bathtub. We provide some of its structural properties. We estimate the parameters by maximum likelihood estimation method, and perform a simulation study to verify the asymptotic properties of the estimator for the inverse Weibull baseline. The practicality of the new APGOGE-Rayleigh model is shown through application to uncensored real dataset.

The Ultraviolet Luminosity Function at 0.6 < z < 1 from UVCANDELS

UVCANDELS is a Hubble Space Telescope Cycle-26 Treasury Program awarded 164 orbits of primary ultraviolet (UV) F275W imaging and coordinated parallel optical F435W imaging in four CANDELS fields—GOODS-N, GOODS-S, EGS, and COSMOS—covering a total area of ∼426 arcmin2. This is ∼2.7 times larger than the area covered by previous deep-field space UV data combined, reaching a depth of about 27 and 28 ABmag (5σ in 0.”2 apertures) for F275W and F435W, respectively. Along with new photometric catalogs, we present an analysis of the rest-frame UV luminosity function (LF), relying on our UV-optimized aperture photometry method, yielding a factor of 1.5 increase over H-isophot aperture photometry in the signal-to-noise ratios of galaxies in our F275W imaging. Using well-tested photometric redshift measurements, we identify 5810 galaxies at redshifts 0.6 < z < 1, down to an absolute magnitude of M UV = −14.2. In order to minimize the effect of uncertainties in estimating the completeness function, especially at the faint end, we restrict our analysis to sources above 30% completeness, which provides a final sample of 4726 galaxies at −21.5 < M UV < −15.5. We performed a maximum likelihood estimate to derive the best-fit parameters of the UV LF. We report a best-fit faint-end slope of α=−1.359−0.041+0.041 at z ∼ 0.8. Creating subsamples at z ∼ 0.7 and z ∼ 0.9, we observe a possible evolution of α with redshift. The unobscured UV luminosity density at M UV < −10 is derived as ρUV=1.339−0.030+0.027(×1026ergs−1Hz−1Mpc−3) using our best-fit LF parameters. The new F275W and F435 photometric catalogs from UVCANDELS have been made publicly available on the Barbara A. Mikulski Archive for Space Telescopes.

Dynamic survival analysis: Modelling the hazard function via ordinary differential equations.

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary differential equations (ODEs). This modelling approach can be used to provide qualitative and quantitative analyses of the evolution of the hazard function over time. Our proposal capitalises on the extensive literature on ODEs which, in particular, allows for establishing basic rules or laws on the dynamics of the hazard function via the use of autonomous ODEs. We show how to implement the proposed modelling framework in cases where there is an analytic solution to the system of ODEs or where an ODE solver is required to obtain a numerical solution. We focus on the use of a Bayesian modelling approach, but the proposed methodology can also be coupled with maximum likelihood estimation. A simulation study is presented to illustrate the performance of these models and the interplay of sample size and censoring. Two case studies using real data are presented to illustrate the use of the proposed approach and to highlight the interpretability of the corresponding models. We conclude with a discussion on potential extensions of our work and strategies to include covariates into our framework. Although we focus on examples of Medical Statistics, the proposed framework is applicable in any context where the interest lies in estimating and interpreting the dynamics of the hazard function.

Identifying a class of Ridge-type estimators in binary logistic regression models

In the analysis of logistic regression models, various biased estimators have been proposed as an alternative to the maximum likelihood estimator (MLE) for estimating model parameters in the presence of multicollinearity. In this study, a new class of biased estimators called Logistic Ridge-type Estimator (LRTE) is proposed by generalizing the existing biased estimators that include two biasing parameters. The performance of the proposed estimator is compared with the other biased estimators in terms of the Matrix Mean Squared Error (MMSE). Two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimator. A numerical example is provided to demonstrate the performance of the proposed biased estimator. The results revealed that LRTE performed better than other existing biased estimators under the conditions investigated in this study.

A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing

Geographically weighted regression (GWR) and its extensions are important local modelling techniques for exploring spatial heterogeneity in regression relationships. However, when dealing with spatial data of overlapping samples – for example, when precise locational information is aggregated to a shared neighbourhood to avoid revealing the addresses of individual survey respondents – GWR-based models can encounter several problems, including obtaining reliable bandwidths. Because data with this characteristic exhibit spatial hierarchical structures, we propose combining hierarchical linear modelling (HLM) with GWR to give a hierarchical and geographically weighted regression (HGWR) model that divides coefficients into sample-level fixed effects, group-level fixed effects, sample-level random effects, and group-level spatially weighted effects. This paper presents a back-fitting likelihood estimator to fit the model, a simulation experiment that suggests that HGWR is better able to capture these effects and the spatial heterogeneity within them than are traditional HLM or GWR models, and a case study looking at predictors of housing price in Beijing, China. The ability of HGWR to tackle both spatial and group-level heterogeneity simultaneously suggests its potential as a promising data modelling tool for handling spatio-temporal big data with spatially hierarchical structures.

Integrating climate change predictions into infrastructure degradation modelling using advanced markovian frameworks to enhanced resilience

This study introduces a prognostic model that quantifies infrastructure degradation in highway systems, incorporating the impacts of climate change using an advanced Markovian framework. By assimilating extensive historical maintenance records and detailed climatic data, the model employs a multi-tiered exponential erosion risk framework to enhance predictive accuracy. Our findings indicate a 15–20% acceleration in degradation rates under projected climate scenarios, emphasizing the necessity for climate-adaptive infrastructure management strategies. Utilizing maximal likelihood estimation, the model corrects sample distortion biases, resulting in a 30% improvement in the accuracy of degradation forecasts compared to conventional models. This accuracy enables maintenance cost savings of up to 25% by optimizing repair timings, thus avoiding premature interventions and reducing costs associated with reactive maintenance strategies. The validated model provides a robust tool for strategic planning and adaptive maintenance of highway systems, promoting resilient infrastructure management in the face of evolving climatic conditions. This research ensures that infrastructure professionals can anticipate and mitigate the impacts of climate change, optimizing maintenance budgets and extending the service life of highway assets.

Comparison of Various Ranking Methods with Pareto Distribution Methods in Imprecise Data

The Pareto distribution has seen wide application in many different fields recently. Nowadays, the data we collect may be imprecise and contain uncertainties. This means that the values we gather cannot necessarily be considered a single, definitive value. In this paper, it is explored how various estimation methods like the method of moments, maximum likelihood estimation, and least squares estimation are used to determine the parameters of a Pareto distribution when the data is fuzzy or uncertain in nature. When making decisions, ranking methods are often heavily relied upon. For this reason, the application of several different ranking techniques to triangular fuzzy numbers (TFNs) is considered. The ranking methods for TFNs are found to tend to produce estimated parameters that are quite similar or even identical. The estimating parameters of a Pareto distribution can be solved for when dealing with fuzziness by the use of ranking methods such as alpha-cut, Yeager’s method, sub-interval method, Pascal method, magnitude method, and centroid method on the TFNs. By comparing the results of these various ranking techniques, an analysis is conducted to whether the estimated parameters of the Pareto distribution are consistent across the different ranking methods for TFNs get the uniqueness of the solution or differ. The decision making done by among the various ranking techniques, which method preferable for future comparison with extended of new ranking techniques. The conclusion is that the simulation results match up well with actual application data, serving as a good example for explaining this overall strategy.

GTRpmix: A Linked General Time-Reversible Model for Profile Mixture Models.

Profile mixture models capture distinct biochemical constraints on the amino acid substitution process at different sites in proteins. These models feature a mixture of time-reversible models with a common matrix of exchangeabilities and distinct sets of equilibrium amino acid frequencies known as profiles. Combining the exchangeability matrix with each profile generates the matrix of instantaneous rates of amino acid exchange for that profile. Currently, empirically estimated exchangeability matrices (e.g. the LG matrix) are widely used for phylogenetic inference under profile mixture models. However, these were estimated using a single profile and are unlikely optimal for profile mixture models. Here, we describe the GTRpmix model that allows maximum likelihood estimation of a common exchangeability matrix under any profile mixture model. We show that exchangeability matrices estimated under profile mixture models differ from the LG matrix, dramatically improving model fit and topological estimation accuracy for empirical test cases. Because the GTRpmix model is computationally expensive, we provide two exchangeability matrices estimated from large concatenated phylogenomic-supermatrices to be used for phylogenetic analyses. One, called Eukaryotic Linked Mixture (ELM), is designed for phylogenetic analysis of proteins encoded by nuclear genomes of eukaryotes, and the other, Eukaryotic and Archaeal Linked mixture (EAL), for reconstructing relationships between eukaryotes and Archaea. These matrices, combined with profile mixture models, fit data better and have improved topology estimation relative to the LG matrix combined with the same mixture models. Starting with version 2.3.1, IQ-TREE2 allows users to estimate linked exchangeabilities (i.e. amino acid exchange rates) under profile mixture models.

A robust electricity price forecasting framework based on heteroscedastic temporal Convolutional Network

Electricity price forecasting (EPF) is a complex task due to market volatility and nonlinearity, which cause rapid and unpredictable fluctuations and introduce heteroscedasticity in forecasting. These factors result in varying prediction errors over time, making it difficult for models to capture stable patterns and leading to poor performance. This study introduces the Heteroscedastic Temporal Convolutional Network (HeTCN), a novel Encoder-Decoder framework designed for day-ahead EPF. HeTCN utilizes a Temporal Convolutional Network (TCN) to capture long-term dependencies and cyclical patterns in electricity prices. A key innovation is the heteroscedastic output layer, which directly represents variable uncertainty, enhancing performance under fluctuating market conditions. Additionally, a multi-view feature selection algorithm identifies crucial factors for specific periods, improving forecast precision. The framework employs an improved loss function based on maximum likelihood estimation (MLE), which adjusts for the heteroscedastic nature of electricity prices by predicting both the mean and variance of the price distribution. This approach mitigates the impact of extreme price spikes and reduces overfitting, resulting in robust and reliable predictions. Comprehensive evaluations demonstrate HeTCN’s superiority over existing solutions such as DeepAR and the Temporal Fusion Transformer (TFT), with average improvements of 25.3%, 24.9%, and 17.4% in the mean absolute error (MAE), symmetric mean absolute percentage error (sMAPE), and the root of mean squared error (RMSE) compared to DeepAR, and 17.6%, 14.4%, and 13.6% relative to TFT across five distinct electricity markets. These results underscore HeTCN’s effectiveness in managing volatility and heteroscedasticity, marking a significant advancement in electricity price forecasting.

Modeling speed behavior of vehicles in school zones under the impact of motorcycle-dominated societies

This study evaluates the free-flow speed of vehicles passing through the 9 school zones in Pleiku City, Vietnam before and after the establishment of the speed limit. The speed data was collected and analyzed by using an image processing technology. The results show that there is a decrease in the speed of vehicles when passing through the school gate, however, it still remains high. After the establishment of the speed limit of 30 kph at the school zone, the speed is likely reduced but not significantly. Furthermore, Maximum Likelihood Estimation method was used to model the speed behavior in the form of normal distribution. The estimated results show a realistic reflection of the observed speed distribution. The results can be applied in making policies to reduce school traffic accidents and to promote active travel on the school journey in countries such as Vietnam or in other countries with relevant contexts.

Analysis of leukemia and forest fires data using new Poisson Quasi-Shanker distribution

In this study, a new two-parameter discrete distribution is introduced by mixing Poisson and Quasi-Shanker distributions. The new model is named Poisson Quasi-Shanker-(PQS) distribution. Some important mathematical properties of the proposed distribution are derived including factorial moments, moment-generating function, variance, and dispersion index. The parameters of PQS distribution are estimated using the maximum likelihood estimation approach. A Monte Carlo simulation is carried out to illustrate the behavior of derived estimators. The applicability of the new model is assessed using two datasets from different areas. It is concluded the proposed distribution is more flexible as compared to the considered competitive distributions.

Maximum likelihood estimation for multi-factor uncertain differential equations

Multi-factor uncertain differential equation (MUDE) is widely used in dynamic systems with multiple types of uncertainties. After observing actual data, how to estimate unknown parameters based on these observations rationally is a key issue. Existing estimation methods are based on difference scheme of MUDE with a prerequisite that observation intervals are small enough. To overcome this shortage, a novel maximum likelihood method is proposed using the concept of residual for MUDE in this work. Both analytical and numerical methods for calculating residuals are also studied. In addition, uncertain hypothesis test is employed to verify the reasonableness of estimations. Numerical example and real data analyses show the proposed method in details.

STATISTICAL INFERENCE ON SINE-EXPONENTIAL DISTRIBUTION PARAMETER

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study’s findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution.

Different sensory information is used for state estimation when stationary or moving.

The accurate estimation of limb state is necessary for movement planning and execution. While state estimation requires both feedforward and feedback information, we focus here on the latter. Prior literature has shown that integrating visual and proprioceptive feedback improves estimates of static limb position. However, differences in visual and proprioceptive feedback delays suggest that multisensory integration could be disadvantageous when the limb is moving. We formalized this hypothesis by modeling feedback-based state estimation using the longstanding maximum likelihood estimation model of multisensory integration, which we updated to account for sensory delays. Our model predicted that the benefit of multisensory integration was largely lost when the limb was passively moving. We tested this hypothesis in a series of experiments in human subjects that compared the degree of interference created by discrepant visual or proprioceptive feedback when estimating limb position either statically at the end of the movement or dynamically at movement midpoint. In the static case, we observed significant interference: discrepant feedback in one modality systematically biased sensory estimates based on the other modality. However, no interference was seen in the dynamic case: participants could ignore sensory feedback from one modality and accurately reproduce the motion indicated by the other modality. Together, these findings suggest that the sensory feedback used to compute a state estimate differs depending on whether the limb is stationary or moving. While the former may tend toward multimodal integration, the latter is more likely to be based on feedback from a single sensory modality.Significance statement The estimation of limb state involves feedforward and feedback information. While estimation based on feedback has been well studied when the limb is stationary, it is unknown if similar sensory processing supports limb position estimates when moving. Using a computational model and behavioral experiments, we show that feedback-based state estimation may involve multisensory integration in the static case, but it is likely based on a single modality when the limb is moving. We suggest that this difference may stem from visual and proprioceptive feedback delays.

Simple closed-form estimation of a binary latent variable model

Abstract This paper develops a closed-form nonparametric estimator of the conditional distribution function for a binary outcome variable given an unobserved latent variable. This type of function is commonly used in models that involve measurement error and dynamic models with agent-specific unobserved heterogeneity. This paper presents a consistent extremum sieve estimator with the following advantages: i) it has a closed-form expression for all the sieve coefficients; ii) it is computationally straightforward, equivalent to computing eigenvalues and eigenvectors of matrices without the use of iterative optimization algorithms. While as flexible as the sieve maximum likelihood estimator (MLE) previously proposed for this model, our estimator proves computationally simpler. The finite sample properties of the estimator are investigated through a Monte Carlo study, and the developed estimator is applied to a probit model to assess the targeting performance of a social welfare program.

How Product Standards Influence Tea Exports? Empirical Evidence from India

India has witnessed a declining trend in tea exports in the recent period, which can partly be attributed to competition from exporters (e.g., Kenya and Sri Lanka) enjoying price advantages over the Indian varieties. However, although after the inception of the World Trade Organization (WTO) in 1995, the tariff barriers on Indian tea exports have come down across developed partners, the incidence of non-tariff barriers (NTBs) has emerged as a challenge in many destinations, with a possible dampening effect on exports. The present analysis attempts to analyse whether the imposition of product standard related measures, particularly sanitary and phytosanitary (SPS) and Technical Barriers to Trade (TBT) interventions, may have negatively influenced Indian tea exports over the period 1996–2021. Rather than considering the mere presence of SPS–TBT standards in major partner countries, their potential impacts on Indian tea exports have been determined by analysing the stringency levels of the corresponding notifications submitted to the WTO. The constructed stringency patterns are then incorporated into the Poisson pseudo maximum likelihood estimation models. The observed negative influence of standard-related measures in partner countries on Indian tea exports calls for policy interventions to enable the sector to better ensure compliance in the future.

CURTAINs flows for flows: Constructing unobserved regions with maximum likelihood estimation

Model independent techniques for constructing background data templates using generative models have shown great promise for use in searches for new physics processes at the LHC. We introduce , a major improvement to the CURTAINs method by training the conditional normalizing flow between two side-band regions using maximum likelihood estimation instead of an optimal transport loss. The new training objective improves the robustness and fidelity of the transformed data and is much faster and easier to train. We compare the performance against the previous approach and the current state of the art using the LHC Olympics anomaly detection dataset, where we see a significant improvement in sensitivity over the original CURTAINs method. Furthermore, CURTAINsF4F requires substantially less computational resources to cover a large number of signal regions than other fully data driven approaches. When using an efficient configuration, an order of magnitude more models can be trained in the same time required for ten signal regions, without a significant drop in performance.

Estimating the risk of major adverse cardiac events following radiotherapy for left breast cancer using a modified generalized Lyman normal-tissue complication probability model

BackgroundWe introduced an adapted Lyman normal-tissue complication probability (NTCP) model, incorporating clinical risk factors and censored time-to-event data, to estimate the risk of major adverse cardiac events (MACE) following left breast cancer radiotherapy (RT). Materials and methodsClinical characteristics and MACE data of 1100 women with left-side breast cancer receiving postoperative RT from 2005 to 2017 were retrospectively collected. A modified generalized Lyman NTCP model based on the individual left ventricle (LV) equivalent uniform dose (EUD), accounting for clinical risk factors and censored data, was developed using maximum likelihood estimation. Subgroup analysis was performed for low-comorbidity and high-comorbidity groups. ResultsOver a median follow-up 7.8 years, 64 patients experienced MACE, with higher mean LV dose in affected individuals (4.1 Gy vs. 2.9 Gy). The full model accounting for clinical factors identified D50 = 43.3 Gy, m = 0.59, and n = 0.78 as the best-fit parameters. The threshold dose causing a 50 % probability of MACE was lower in the high-comorbidity group (D50 = 30 Gy) compared to the low-comorbidity group (D50 = 45 Gy). Predictions indicated that restricting LV EUD below 5 Gy yielded a 10-year relative MACE risk less than 1.3 and 1.5 for high-comorbidity and low-comorbidity groups, respectively. ConclusionPatients with comorbidities are more susceptible to cardiac events following breast RT. The proposed modified generalized Lyman model considers nondosimetric risk factors and addresses incomplete follow-up for late complications, offering comprehensive and individualized MACE risk estimates post-RT.

Transient and Persistent Technical Efficiencies in Rice Farming: A Generalized True Random-Effects Model Approach

This study estimates transient and persistent technical efficiencies (TEs) using a generalized true random-effects (GTRE) model. We estimate the GTRE model using maximum likelihood and Bayesian estimation methods, then compare it to three simpler models nested within it to evaluate the robustness of our estimates. We use a panel data set of 945 observations collected from 344 rice farming households in Vietnam’s Mekong River Delta. The results indicate that the GTRE model is more appropriate than the restricted models for understanding heterogeneity and inefficiency in rice production. The mean estimate of overall technical efficiency is 0.71 on average, with transient rather than persistent inefficiency being the dominant component. This suggests that rice farmers could increase output substantially and would benefit from policies that pay more attention to addressing short-term inefficiency issues.