Parameter Estimation Research Articles

ON ESTIMATIONS IN AN EQUATION WITH A PARAMETER AND A DISCONTINUOUS OPERATOR

In a real reflexive Banach space, an equation with a parameter and a discontinuous nonlinear operator is considered. Both parameter estimations and operator norms are found for the equation. These estimations validate and define concretely the similar estimations obtained earlier in problems with a parameter for elliptic and ordinary differential equations with discontinuous right-hand sides.

Apertura Comercial Y Crecimiento Económico: Una Aproximación Empírica

Economic growth has beneficial effects on the general well-being of a society. Identifying and analysing its determining factors becomes essential to improve economic policy decisions. Among these factors, the effects of trade openness are widely debated in the literature. Although there are many works that study the relationship between trade openness and economic growth, the results are heterogeneous and differ depending on the level of development of the economies, the openness variable considered, among other conditions. The main objective of this paper is to investigate the existence of a relationship between trade openness and economic growth in a large group of developed and developing countries, considering different openness measures, and thus outline recommendations for economic policies that promote growth. The central hypothesis is that trade openness has a different effect on the economic growth rate depending on the degree of development of the economies and the openness variable analysed. To meet the objective, parametric estimates were used for the period 1960-2019, and alternative measures of openness were constructed to the conventional indicator defined as the sum of exports and imports in relation to the gross domestic product (GDP). The results obtained in this work differ depending on the level of development of the countries analysed and the openness measures used.

The power of effect size stabilization.

Determining an appropriate sample size in psychological experiments is a common challenge, requiring a balance between maximizing the chance of detecting a true effect (minimizing false negatives) and minimizing the risk of observing an effect where none exists (minimizing false positives). A recent study proposes using effect size stabilization, a form of optional stopping, to define sample size without increasing the risk of false positives. In effect size stabilization, researchers monitor the effect size of their samples throughout the sampling process and stop sampling when the effect no longer varies beyond predefined thresholds. This study aims to improve our understanding of effect size stabilization properties. Simulations involving effect size stabilization are presented, with parametric modulation of the true effect in the population and the strictness of the stabilization rule. As previously demonstrated, the results indicate that optional stopping based on effect-size stabilization consistently yields unbiased samples over the long run. However, simulations also reveal that effect size stabilization does not guarantee the detection of a true effect in the population. Consequently, researchers adopting effect size stabilization put themselves at risk of increasing type 2 error probability. Instead of using effect-size stabilization procedures for testing, researchers should use them to reach accurate parameter estimates.

Bubble Detection in Multiphase Flows Through Computer Vision and Deep Learning for Applied Modeling

An innovative method for bubble detection and characterization in multiphase flows using advanced computer vision and neural network algorithms is introduced. Building on the research group’s previous findings, this study combines high-speed video capture with advanced deep learning techniques to enhance bubble detection accuracy and dynamic analysis. In order to further develop a robust framework for detecting and analyzing bubble properties in multiphase flows, enabling accurate estimation of essential mass transfer parameters, a YOLOv9-based neural network was implemented for bubble segmentation and trajectory analysis, achieving high accuracy. Key contributions include the development of an averaged mass transfer model integrating experimental data, neural network outputs, and scaling algorithms, as well as validation of the proposed methodology through experimental studies, including high-speed video imaging and comparisons with mass transfer coefficients obtained via the sulfite method. By precisely characterizing critical parameters, the algorithm enables accurate gas transfer rate calculations, ensuring optimal conditions in various industrial applications. The neural network-based algorithm serves as a non-invasive platform for detailed characterization of bubble media, demonstrating high accuracy in experimental validation and significantly outperforming traditional techniques. This approach provides a robust tool for real-time monitoring and modeling of bubble flows, laying the foundation for novel, non-invasive methods to measure multiphase media properties.

Estimating the Generalizations of Process Capability Index Cpmk$C_{pmk}$ in the Presence of Outliers

ABSTRACTProcess capability indices (PCIs) play a fundamental role in assessing and quantifying the capability of manufacturing processes to meet customer specifications. To date, the majority of PCIs that are now in use have been examined through the use of novel generalizations of PCIs with symmetric tolerances to check the performance of an industrial manufacturing process. In this paper, we proposed new estimations of some indices with asymmetric tolerances in the presence of outliers. New robust and parametric estimators of some PCIs are introduced to estimate and compare these indices for each normal distribution with the presence of different outliers. Meanwhile, this paper discusses how well the proposed method can be used for non‐normal data. For illustration purpose, the application example is presented.

Finite‐Dimensional Adaptive Observer Design for Reaction Diffusion Equation With Large Output Delay

ABSTRACTThe goal of this paper is to present a new finite‐dimensional adaptive observer for some uncertain linear parabolic systems with delayed measurements. The observer is based on the modal decomposition approach and uses a classical persistent excitation condition. We prove that by using a finite‐dimensional state predictor, we ensure exponential convergence of both states parameters estimation error for arbitrary long constant delay.

Bounded Multivariate Contaminated Normal Mixture Model with an Application in Skin Cancer Detection

Introduction: In real-world datasets, outliers are a common occurrence that can have a significant impact on the accuracy and reliability of statistical analyses. Detecting these outliers and developing robust models to handle their presence is a crucial challenge in data analysis. For instance, natural images may have complex distributions of values due to environmental factors like noise and illumination, resulting in objects with overlapping regions and non-trivial contours that cannot be accurately described by Gaussian mixture models. In many real life applications, observed data always fall in bounded support regions. This leads to the idea of bounded support mixture models. Motivated by the aforementioned observations, we introduce a bounded multivariate cntaminated normal distribution for fitting data with non-Gaussian distributions, asymmetry, and bounded support which makes finite mixture models more robust to fitting, since rare observations are given less importance in calculations. Methods: A family of finite mixtures of bounded multivariate contaminated normal distributions is introduced. The model is well-suited for computer vision and pattern recognition problems due to its heavily-tailed and bounded nature, providing flexibility in modeling data in the presence of outliers. A feasible expectation- maximization algorithm is developed to compute the maximum likelihood estimates of the model parameters using a selection mechanism. Results: The proposed methodology is validated by conducting experiments on both simulated data and two real natural skin cancer images. We estimate the parameters by the proposed expectation-maximization algorithm. The obtained results shown that the proposed model has successfully enhanced accuracy in segmenting skin lesions. Conclusion: The reliable model-based clustering using finite mixtures of bounded multivariate contaminated normal distributions is introduced. An expectation-maximization algorithm was created to estimate parameters, with closed-form expressions utilized at the E-step. Practical tests on images for skin cancer detection showed enhanced accuracy in delineating skin lesions.

Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progres- sively Type-II Censored Data

Introduction: Stress-strength models has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, biology, genetics, medicine etc. This paper investigates estimation of the stress-strength reliability parameter R=P(Y<X) in two-parameter exponential distributions under progressively type-II censored samples. Methods: The maximum likelihood and the best linear unbiased estimates of P(Y<X) are obtained, and the Bayes estimates of P(Y<X) are computed under the squared error, linear-exponential, and Stein loss functions. Also, confidence intervals of stress-strength reliability such as the bootstrap confidence intervals, highest posterior density credible interval, and confidence interval based on the generalized pivotal quantity are obtained. Results: Using a simulation study, the point estimators and confidence intervals are evaluated and compared. A set of real data is presented for better clarification of the issue. Conclusion: The results demonstrated that with increasing the sample size, in almost cases the estimated risk of all the estimators decrease. Also, in almost all cases the Bayes estimator under the linear-exponential loss function has smaller estimated risk than the other estimators. Based on our simulation, the expected lengths of all intervals tend to decrease when the sample size increases. Moreover, the highest posterior density confidence intervals are shorter than the others intervals for all the values of P(Y<X).

Longitudinal studies: focus on trajectory analysis in kidney diseases.

Longitudinal cohort studies are pivotal in medical research for understanding disease progression over time. These studies track a group of individuals across multiple time points, enabling the identification of risk factors and the evaluation of interventions. Traditional methods like linear mixed models, generalized estimating equations, and survival analysis often fall short in capturing the complex, non-linear patterns of disease progression. Trajectory analysis, a statistical technique that identifies distinct paths within longitudinal data, offers a more nuanced approach. This review delves into the methodological foundations of trajectory analysis, including data preparation, model selection, parameter estimation, model evaluation, and interpretation. It highlights the advantages of trajectory analysis, such as its ability to capture heterogeneity, handle various data types, and enhance predictive power. The application of trajectory analysis in nephrology, particularly in chronic kidney disease and diabetic nephropathy, demonstrates its utility in identifying distinct subgroups with different disease trajectories. Studies have shown that trajectory analysis can uncover patterns of renal function decline and proteinuria progression, providing insights that inform personalized treatment strategies. Despite its strengths, trajectory analysis requires advanced statistical knowledge, computational resources, and large sample sizes, which can be barriers for some researchers. Nevertheless, its ability to reveal complex disease patterns and improve predictive accuracy makes it a valuable tool in longitudinal studies. This review underscores the potential of trajectory analysis to enhance our understanding of disease progression and improve patient outcomes in nephrology and beyond.

Efficient and Robust Estimation of Various Ore and Mineral Model Parameters from Residual Gravity Anomalies Using the Dual Classification Learning Rao Algorithm

Efficient and Robust Estimation of Various Ore and Mineral Model Parameters from Residual Gravity Anomalies Using the Dual Classification Learning Rao Algorithm

Are Historically Black Colleges and Universities an Ecosystem for Black Entrepreneurship? Some Evidence From the Brookings Institution 2022 Black Progress Index Data

Historically, Black Americans have owned businesses at a lower rate than White Americans. While there is a vast literature on the factors that explain this disparity, machine-learning analytics have not been exploited to capture relevant predictive determinants of the formation of Black-owned Businesses. In this paper, we utilize the Brookings Institution 2022 Black Progress Index Data to explore, similar to the approaches in criminology, the attractors and generators of Black-owned businesses across US counties. We augment the Brookings data to account for the presence of a Historically Black College/University (HBCU) in the county, and deploy a rigorous least absolute shrinkage and selection operator—a machine-learning analytical tool—to identify the best predictors of Black-owned businesses in a county, and classify them as attractors and/or generators in regression specifications. Parameter estimates from several mixed effects regressions specifications reveal that HBCUs are an attractor/generator of Black entrepreneurship. Treatment effect matching parameter estimates suggest that the HBCU effects on Black entrepreneurship outcomes are causal. Overall, our findings suggest that HBCUs constitute an ecosystem for Black entrepreneurship as they are an important catalyst and driver of Black-owned businesses, and can serve a substantive role in reducing racial entrepreneurship disparities. Our results suggest that policies that engender private or public investments in HBCU capacity to enhance their Black entrepreneurship ecosystem can be effective in reducing Black-White disparities in entrepreneurship and business ownership.

Тhermal history and fluid regime during the formation of Eldjurta massif of biotite granites (Greater Caucasus): reconstructions based on isotope (δ<sup>18</sup>О, δD) and geochemical data

Based on the geochemical and isotopic (δ18О, δD) data the thermal and fluid conditions during the formation of the Eldjurta granite massif were reconstructed. Analysis of rocks collected from the core of the Tyrnyauz Superdeep Well (TSW) within the depth range of 1427–3923 m revealed their homogeneous isotopic parameters: the δ18О values of bulk samples, quartz, feldspars, and biotite in 12 samples of biotite granites are 8.50 ± 0.33, 9.55 ± 0.22, 8.40 ± 0.33 and 5.45 ± 0.40‰, respectively. The δD values in the biotite vary from −103.3 to −95.6‰. The closure temperatures of the oxygen isotope system of quartz are 440–980°C. The rock cooling history was reconstructed using a new approach based on the analysis of single quartz grains. This approach can be used for detailed reconstructions of thermal history during formation of intrusive bodies. The definite samples were used to demonstrate that Dodson’s equation is valid for description of the δ18О values of quartz in a granite system. The data obtained suggest that the studied part of the massif was formed in at least two almost simultaneous stages. The lower part of the massif was crystallized first, and the second injection of granite melt arrived immediately after the first portion has been crystallized, but had no yet had time to cool significantly. The Тс values in the lower part of the massif indicate the reopening of the oxygen isotope system of quartz, with subsequent long-term isotope re-equilibration between minerals. This leads to decrease of the observed Тс values and the calculated cooling rates, which is related to increasing volume of the intrusive body and cooling within already heated rocks. Estimates of the isotopic parameters of the water component indicate the absence of exotic water fluid (meteoric or buried waters) during cooling of the massif. The variations of the δ18О values in the minerals of the Eldjurta biotite granites can be described only in terms of a simple retrograde exchange at the cooling stage

Renewable Energy, Financial Growth and Technological Progress: Analyzing the Dynamics of Sectoral Emissions in Pakistan

The study examined the role of renewable energy, financial growth, and technical progress in Pakistan's industrial, manufacturing, and service sector emissions. The study collected consistent time series data from 1975 to 2022 and employed the ARDL-Bounds testing approach to estimate the short- and long-term parameter estimates. The study assessed three broad models. The first model linked renewable energy to carbon emissions in the cement industry. Carbon emissions and renewable energy were negatively related. Further, a negative relationship exists between information and communication technologies (ICTs) and carbon emissions, with a one-unit increase in ICT reducing CO2 emissions by 0.135 units. A substantial and positive association was found between GDP per capita and CO2 emissions in Pakistan. At the same time, the square term decreases carbon emissions, supporting a country's environmental Kuznets curve (EKC) hypothesis. In the second model, high technology exports were positively connected with manufacturing CO2 emissions, while energy use's interaction term had a significant negative impact. Manufacturing CO2 emissions were positively correlated with renewable energy in the short and medium term. Financial development is assessed by money supply, which directly affects carbon emissions to support financial-led emissions in a country. The third model used GHG emissions as the dependent variable and focused on the service sector. The interaction term between energy consumption and clean fuel technology (CFT) was negative and significant, although GHG emissions and CFT were positively correlated. Non-renewable energy raised GHG emissions, while renewable energy decreased them.

Estimation of stress-strength reliability based on unit generalized Gompertz distribution

Although the investigation of the stress-strength parameter has a long history due to its importance, the investigation of this parameter in distributions with a limited range, such as (0, 1), has received less attention. Thus, in this article, we study the stress-strength parameter for Unit Generalized Gompertz (UGG) distribution, which can cover a variety of data, including data skewed ones. Considering the flexibility of the shape of the density function and its hazard rate function, we expect that this distribution would possess more applicability and can be fitted to different data sets. With this aim, we discuss the parameter R for the UGG distribution and obtain different methods of parameter estimation such as maximum likelihood, bootstrap, and Bayesian. The performance of the estimators has been done by simulation, and finally, the presented content has been applied to a real data set.

Gwforge: A user-friendly package to generate gravitational-wave mock data

Abstract The next-generation gravitational-wave detectors, with their improved sensitivity and wider frequency bandwidth, will be capable of observing almost every compact binary signal from epochs before the first stars began to form, increasing the number of detectable binaries to hundreds of thousands annually. This will enable us to observe compact objects through cosmic time, probe extreme matter phenomena, do precision cosmology, study gravity in strong field dynamical regimes and potentially allow observation of fundamental physics beyond the standard model. However, the richer data sets produced by these detectors will pose new computational, physical and astrophysical challenges, necessitating the development of novel algorithms and data analysis strategies. To aid in these efforts, this paper introduces gwforge, a user-friendly, lightweight Python package, to generate mock data for next-generation detectors. We demonstrate the package's capabilities through data simulation examples and highlight a few potential applications: performance loss due to foreground noise, bright-siren cosmology and impact of waveform systematics on binary parameter estimation.

Probabilistic parameter estimation and reliability assessment of nonlinear structures based on generative adversarial networks with Gaussian process regression

Probabilistic parameter estimation and reliability assessment of nonlinear structures based on generative adversarial networks with Gaussian process regression

Invariance transformations in wave-optics lensing: Implications for gravitational-wave astrophysics and cosmology

Gravitational lensing offers unique opportunities to learn about the astrophysical origin of distant sources, the abundance of intervening objects acting as lenses, and gravity and cosmology in general. However, all this information can only be retrieved as long as one can disentangle each effect from the finite number of observables. In the geometric optics regime, typical of electromagnetic radiation, when the wavelength of the lensed signal is small compared to the size of the lens, there are invariance transformations that change the mass of the lens and the source-lens configuration but leave the observables unchanged. Neglecting this “mass-sheet degeneracy” can lead to biased lens parameters or unrealistic low uncertainties, which could then transfer to an incorrect cosmography study. This might be different for gravitational waves as their long wavelengths can be comparable to the lens size and lensing enters into the wave-optics limit. We explore the existence of invariance transformations in the wave-optics regime of gravitational-wave lensing, extending previous work and examining the implications for astrophysical and cosmological studies. We study these invariance transformations using three different methods of increasing level of complexity: template mismatch, Fisher Matrix, and Bayesian parameter estimation. We find that, for a sufficiently loud signal, the degeneracy is partially broken and the lens and cosmological parameters, e.g. H0, can be retrieved independently and unbiased. In current ground-based detectors, though, considering also population studies, a strong constraint on these parameters seems quite remote and the prevailing degeneracy implies a larger uncertainty in the lens model reconstruction. However, with better sensitivity of the third-generation ground-based detectors, a meaningful constraint on H0 is possible to obtain. Published by the American Physical Society 2024

Relative humidity prediction across the Indian subcontinent using Kumaraswamy distribution based non-Gaussian model.

Relative humidity (RH) significantly influences various aspects of human life, including agriculture, weather prediction, indoor air quality, and energy consumption. Its intricate non-linear behavior poses a significant challenge for accurate estimation. In the context of Indian climate change, precise forecasting of RH is vital for agriculture and weather prediction. This study proposes a new non-Gaussian approach, the Kumaraswamy seasonal autoregressive moving average (KSARMA) model, for RH prediction across India's five climatic zones (hot-dry, warm-humid, moderate, cold, and composite). Analyzing monthly RH data from 1981 to 2021, model selection was based on diagnostic analysis and Akaike's information criterion (AIC), with parameter estimation utilizing conditional maximum likelihood estimators (CMLE). The KSARMA model demonstrated superior predictive accuracy compared to other models (e.g., multilayer perceptron, SARIMA, Holt-Winter, and SARMA) across all climatic zones, except the hot-dry zone, as supported by error metrics including RMSE (0.04-0.12), MAE (0.03-0.1), SMAPE (0.04-0.2), and MASE (0.5-.08).

Abundance-mediated species interactions.

Species interactions shape biodiversity patterns, community assemblage, and the dynamics of wildlife populations. Ecological theory posits that the strength of interspecific interactions is fundamentally underpinned by the population sizes of the involved species. Nonetheless, prevalent approaches for modeling species interactions predominantly center around occupancy states. Here, we use simulations to illuminate the inadequacies of modeling species interactions solely as a function of occupancy, as is common practice in ecology. We demonstrate erroneous inference into species interactions due to error in parameter estimates when considering species occupancy alone. To address this critical issue, we propose, develop, and demonstrate an abundance-mediated interaction framework designed explicitly for modeling species interactions involving two or more species from detection/non-detection data. We present Markov chain Monte Carlo (MCMC) samplers tailored for diverse ecological scenarios, including intraguild predation, disease- or predator-mediated competition, and trophic cascades. Illustrating the practical implications of our approach, we compare inference from modeling the interactions in a three-species network involving coyotes (Canis latrans), fishers (Pekania pennanti), and American marten (Martes americana) in North America as a function of occupancy states and as a function of abundance. When modeling interactions as a function of abundance rather than occupancy, we uncover previously unidentified interactions. Our study emphasizes that accounting for abundance-mediated interactions rather than simple co-occurrence patterns can fundamentally alter our comprehension of system dynamics. Through an empirical case study and comprehensive simulations, we demonstrate the importance of accounting for abundance when modeling species interactions, and we present a statistical framework equipped with MCMC samplers to achieve this paradigm shift in ecological research.

Semen Quality Correlation with Seminal Biochemistry and Enzymatic Profile of Barbari and Sirohi Bucks under Sub Tropical Environment

Background: The objective was to study the effect of seasonal variation on reproductive parameters, biochemical parameters and enzymes activity in relation to buck semen quality which would assist to produce good quality sperm doses for artificial insemination in goat farming. Methods: Four ejaculates fortnightly were collected from adult breeding Sirohi and Barbari bucks during summer and winter season by using artificial vagina for the study. Average meteorological data were recorded during the study. Reproductive parameters (scrotal temperature and scrotal circumference) were recorded and fresh semen samples were used for evaluation of sperm attributes (semen volume, pH, sperm concentration, mass motility, individual activity and live-dead sperm count). The seminal plasma was separated by from semen for estimation of different biochemical parameters (Total protein, Albumin, Total cholesterol and Calcium) and seminal enzymes activity (ALT, AST, ALP and LDH). Result: It was observed that sperm attributes and biochemical parameters were significantly (p less than 0.05) increased during winter as compared to summer season in both breed. No significant difference was observed for ALT in both breeds and seasons. Whereas, in summer AST activity was significantly (p less than 0.05) lower than winter in both the breeds. In summer season ALP and LDH activity were significantly (p less than 0.05) higher than winter in both the breeds. A positive correlation had observed with seminal biochemical parameters whereas a negative correlation with ALP and LDH. In conclusion, season influenced the semen quality in Barbari and Sirohi bucks and good quality semen produce during winter as compared to summer.