Estimation Of Linear Models Research Articles

Bayesian grouping-Gibbs sampling estimation of high-dimensional linear model with non-sparsity

In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients β∈Rp. However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions β into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (k) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.

Dual-Arm Space Robot On-Orbit Operation of Auxiliary Docking Prescribed Performance Impedance Control

The impedance control of a dual-arm space robot in orbit auxiliary docking operation is studied. First, for the closed-chain hybrid system formed by the dual-arm space robot after capture operation, the dynamic equation of position uncontrolled and attitude controlled is established. The second-order linear impedance model and second-order approximate environment model are established for the problem of simultaneous output force/pose control of the end of the manipulator. Then, aiming at the transient performance control requirements of the dual-arm space robot auxiliary docking operation in orbit, a sliding mode controller with equivalent replacement of tracking errors is designed by introducing Prescribed Performance Control (PPC) theory. Next, Radial Basis Function Neural Networks (RBFNN) are used to accurately compensate for the modeling uncertainties of the system. Finally, the stability of the system is verified by Lyapunov stability determination. The simulation results show that the attitude control accuracy is better than 0.5°, the position control accuracy is better than 10−3 m, and the output force control accuracy is better than 0.5 N when it reaches 30 N. It also indicated that the proposed control algorithm can limit the transient performance of the controlled system within the preset range and achieve high-precision force/pose control, which ensures a more stable on-orbit auxiliary docking operation of the dual-arm space robot.

Bayesian stein-type shrinkage estimators in high-dimensional linear regression models

Bayesian stein-type shrinkage estimators in high-dimensional linear regression models

Quantile-based robust Kibria–Lukman estimator for linear regression model to combat multicollinearity and outliers: Real life applications using T20 cricket sports and anthropometric data

The performance of ordinary least squares (OLS) and ridge regression (RR) are influenced when outliers are present in y-direction with multicollinearity among independent variables. The robust RR with ridge parameters provides a biased estimator that has a smaller variance than conventional OLS and RR estimators. The optimal value of the ridge parameter has a vital role in bias-variance tradeoff. This study proposes quantile-based estimation of ridge parameter in robust RR to deal with the joint issue of y-direction outliers and multicollinearity. The effectiveness of the proposed estimators is evaluated using intensive Monte Carlo simulation and two real data sets in terms of mean square error (MSE) and predictions sum of squared error (PSSE) criterion. Simulation findings reveal that the newly developed estimators of ridge parameter in robust RR have better performance than OLS, RR, and existing robust RR estimators when errors are normally and non-normally distributed. The results from two numerical examples of T20 Cricket sports and anthropometric data show that the new estimator with quantile probability 0.50 and 0.99 respectively has winning performance among all competing and proposed estimators.

Moment-Based Estimation of Linear Panel Data Models with Factor-Augmented Errors

Abstract I compare two popular methods of estimation for linear panel data models with unobserved factors: the first eliminates the factors with a parameterized quasi-long-differencing (QLD) transformation. The other, referred to as common correlated effects (CCE), uses cross-sectional averages of the data to proxy for the factor space. I show that the CCE assumptions imply unused moment conditions that can be exploited by the QLD transformation. I also derive new linear estimators that weaken identifying assumptions and have desirable theoretical properties. Unlike CCE, these estimators do not require the number of covariates to be less than the number of time periods. I provide the first proof of a fixed-T consistent mean group estimator for heterogeneous linear models with interactive fixed effects. I investigate the effects of per-student expenditure on standardized test performance using data from the state of Michigan.

Locally sparse estimator for functional linear panel models with fixed effects

Locally sparse estimator for functional linear panel models with fixed effects

A New Approach for Prediction of Foliar Dust in a Coal Mining Region and Its Impacts on Vegetation Physiological Processes Using Multi‐Source Satellite Data Sets

AbstractEstimating foliar dust (FD) is essential in understanding the complex interaction between FD, vegetation, and the environment. The elevated FD has a significant impacts on vegetation physiological processes. The present study aims to explore the potential of multi‐sensor optical satellite data sets (e.g., Landsat‐8, 9; Sentinel‐2B, and PlanetScope) in conjunction with in situ data sets for FD estimation over the Jharsuguda coal mining region in Eastern India. The efficacy of different spectral bands and various radiometric indices (RIs) was tested using linear regression models for FD estimation. Furthermore, the study attempts to quantify the impacts of FD on vegetation's physiological processes (e.g., carbon uptake, transpiration, water use efficiency, leaf temperature) through proxy data sets. The key findings of the study uncovered sensor‐specific and common trends in vegetation spectral profiles under varying FD concentrations. A saturation threshold was observed around 50 g/m2 of FD concentration, beyond which additional FD concentration exhibited limited impact on spectral reflectance. On the other hand, the assessment of FD estimation models revealed distinct performances and shared trends across various satellite sensors. Notably, near‐infrared and shortwave infrared‐1 bands, along with certain RIs, such as the Global Environmental Monitoring Index and the Non‐Linear Index, emerged as pivotal for accurate FD estimation. Besides, the study results revealed that vegetation‐associated carbon uptake experienced a ∼2 to 3 gC reduction for every additional gram of FD per square meter. Moreover, the vegetation transpiration reduction per unit of FD ranged from approximately 0.0005 to 0.0006 mm/m2/day, highlighting a moderate impact on transpiration levels. These findings aid a significant evidence base to our understanding of FD's impact on vegetation physiological processes.

A comparative study of linear and nonlinear regression models for blood glucose estimation based on near-infrared facial images from 760 to 1650 nm wavelength

A comparative study of linear and nonlinear regression models for blood glucose estimation based on near-infrared facial images from 760 to 1650 nm wavelength

Weighted expectile average estimation of linear models with missing covariates

In this article, we proposed a weighted expectile average estimator for linear models with missing covariates. The asymptotic normality of the proposed estimator was established in theory. Further, we derived the explicit optimal weight and thus obtained the resulted optimal weighted expectile estimator. In order to examine the finite-sample performance of the proposed estimator, simulation studies and a real data analysis were conducted and the results were compared with other existing competitors in the literature.

Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.

Probabilistic Record Linkage for Families (PRLF): A Discussion of the Development and Validation of this Open-Source Linkage Tool

Linking administrative records across programs can yield person-centered information, including client characteristics, public service trajectories, and outcomes and help to answer policy-related questions. Several solutions are available for undertaking record linkage, producing linkage keys for merging data sources for positively matched pairs of records. In this session, we will demonstrate a new application of the Python RecordLinkage package to family-based record linkages with machine learning algorithms for probability scoring, which we call probabilistic record linkage for families (PRLF). First, we will demonstrate the utility of PRLF with a simulation of administrative records and assess linkage accuracy with variations in match rates and data degradation. Second, we will compare generalized linear model estimates across three record linkage solutions (PRLF, ChoiceMaker, and Link Plus). Findings from the simulation study indicate linkage accuracy is largely influenced by degradation (e.g., missing data fields, erroneous or incomplete values) compared to the proportion of simulated matches between datasets. Results from the methods comparison using real world data indicate that all three solutions, when optimized, provide similar results for researchers. We discuss the strengths of our process, such as the use of ensemble methods, to improve match accuracy. We then will identify caveats of record linkage in the context of administrative data. The tool was developed in Python to allow for researchers to work with open-source software and adjust the basic workflow to fit their linkage needs. We will identify several partnerships where this collaboration has worked successfully and empower attendees with access to this useful tool.

Distributed non-disclosive validation of predictive models by a modified ROC-GLM

BackgroundDistributed statistical analyses provide a promising approach for privacy protection when analyzing data distributed over several databases. Instead of directly operating on data, the analyst receives anonymous summary statistics, which are combined into an aggregated result. Further, in discrimination model (prognosis, diagnosis, etc.) development, it is key to evaluate a trained model w.r.t. to its prognostic or predictive performance on new independent data. For binary classification, quantifying discrimination uses the receiver operating characteristics (ROC) and its area under the curve (AUC) as aggregation measure. We are interested to calculate both as well as basic indicators of calibration-in-the-large for a binary classification task using a distributed and privacy-preserving approach.MethodsWe employ DataSHIELD as the technology to carry out distributed analyses, and we use a newly developed algorithm to validate the prediction score by conducting distributed and privacy-preserving ROC analysis. Calibration curves are constructed from mean values over sites. The determination of ROC and its AUC is based on a generalized linear model (GLM) approximation of the true ROC curve, the ROC-GLM, as well as on ideas of differential privacy (DP). DP adds noise (quantified by the ℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _2$$\\end{document} sensitivity Δ2(f^)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _2(\\hat{f})$$\\end{document}) to the data and enables a global handling of placement numbers. The impact of DP parameters was studied by simulations.ResultsIn our simulation scenario, the true and distributed AUC measures differ by ΔAUC<0.01\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ ext {AUC} < 0.01$$\\end{document} depending heavily on the choice of the differential privacy parameters. It is recommended to check the accuracy of the distributed AUC estimator in specific simulation scenarios along with a reasonable choice of DP parameters. Here, the accuracy of the distributed AUC estimator may be impaired by too much artificial noise added from DP.ConclusionsThe applicability of our algorithms depends on the ℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _2$$\\end{document} sensitivity Δ2(f^)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _2(\\hat{f})$$\\end{document} of the underlying statistical/predictive model. The simulations carried out have shown that the approximation error is acceptable for the majority of simulated cases. For models with high Δ2(f^)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _2(\\hat{f})$$\\end{document}, the privacy parameters must be set accordingly higher to ensure sufficient privacy protection, which affects the approximation error. This work shows that complex measures, as the AUC, are applicable for validation in distributed setups while preserving an individual’s privacy.

Strong laws for weighted sums of widely orthant dependent random variables and applications

Abstract In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

Pengaruh Layanan Agen Pegadaian dan Digital Service terhadap Kinerja PT Pegadaian Cabang Kupang

This research aims to determine the influence of pawnshop agent services and digital services on the performance of PT Pegadaian Kupang Branch. The type of research used is quantitative research using primary data. The sampling technique used in this research was saturated sampling. So in this study the sample used was the entire population, namely pawnshop agents. The data analysis techniques used in this research include instrument testing, multiple linear regression model estimation, classical assumption testing and hypothesis testing using eviews12 software. The results of this research show that the pawnshop agent variable has an influence on the performance of PT Pegadaian Kupang Branch, the digital service variable has an influence on the performance of PT Pegadaian Kupang Branch. So simultaneously the pawnshop agent and digital services variables influence the performance of PT Pegadaian Kupang Branch.

How a population-based cohort of men estimate lifetime risk of prostate cancer in a survey before entering a prostate cancer screening trial in Sweden?

ObjectivesInvestigating men’s perceived lifetime risk of prostate cancer.DesignSurvey-based study to men invited for prostate-specific antigen (PSA) screening in the GÖTEBORG-2 trial between September 2015 and June 2020.Setting38 775 men in...

A new general biased estimator in linear measurement error model

Numerous biased estimators are known to circumvent the multicollinearity problem in linear measurement error models. This article proposes a general biased estimator with the ridge regression and the Liu estimators as special cases. The efficiency of the suggested estimator is compared with ridge regression and Liu estimators under the mean squared error matrix criterion. In addition, a Monte Carlo simulation study and a numerical evaluation have been conducted to elucidate the superiority of the new general biased estimator over other estimators.

Estimation of quality variables in a continuous train of reactors using recurrent neural networks-based soft sensors

The first stage in the industrial production of Styrene-Butadiene Rubber (SBR) typically consists in obtaining a latex from a train of continuous stirred tank reactors. Accurate real-time estimation of some key process variables is of paramount importance to ensure the production of high-quality rubber. Monitoring the mass conversion of monomers in the last reactor of the train is particularly important. To this effect, various soft sensors (SS) have been proposed, however they have not addressed the underlying complex dynamic relationships existing among the process variables. In this work, a SS based on recurrent neural networks (RNN) is developed to estimate the mass conversion in the last reactor of the train. The main challenge is to obtain an adequate estimate of the conversion both in its usual steady-state operation and during its frequent transient operating phases. Three architectures of RNN: Elman, GRU (Gated Recurrent Unit), and LSTM (Long Short-Term Memory) are compared to critically evaluate their performances. Moreover, a comprehensive analysis is conducted to assess the ability of these models to represent different operational modes of the train. The results reveal that the GRU network exhibits the best performance for estimating the mass conversion of monomers. Then, the performance of the proposed model is compared with a previously-developed SS, which was based on a linear estimation model with a Bayesian bias adaptation mechanism and the use of Control Charts for decision-making. The model proposed here proved to be more efficient for estimating the mass conversion of monomers, particularly during transient operating phases. Finally, to evaluate the methodology utilized for designing the SS, the same RNN architectures were trained to online estimate another quality variable: the mass fraction of Styrene bound to the copolymer. The obtained results were also acceptable.

A Bayesian incorporated linear non-Gaussian acyclic model for multiple directed graph estimation to study brain emotion circuit development in adolescence.

Emotion perception is essential to affective and cognitive development which involves distributed brain circuits. Emotion identification skills emerge in infancy and continue to develop throughout childhood and adolescence. Understanding the development of the brain's emotion circuitry may help us explain the emotional changes during adolescence. In this work, we aim to deepen our understanding of emotion-related functional connectivity (FC) from association to causation. We proposed a Bayesian incorporated linear non-Gaussian acyclic model (BiLiNGAM), which incorporated association model into the estimation pipeline. Simulation results indicated stable and accurate performance over various settings, especially when the sample size was small. We used fMRI data from the Philadelphia Neurodevelopmental Cohort (PNC) to validate the approach. It included 855 individuals aged 8-22 years who were divided into five different adolescent stages. Our network analysis revealed the development of emotion-related intra- and intermodular connectivity and pinpointed several emotion-related hubs. We further categorized the hubs into two types: in-hubs and out-hubs, as the center of receiving and distributing information, respectively. In addition, several unique developmental hub structures and group-specific patterns were discovered. Our findings help provide a directed FC template of brain network organization underlying emotion processing during adolescence.

Noise covariance estimation in multi-task high-dimensional linear models

Noise covariance estimation in multi-task high-dimensional linear models

Empirical Analysis of Sustainable Performance in Relation to Stock Exchange Performance: Evidence from Romania

Given the substantial advancements in worldwide financial markets and the sharp increase in sustainability concerns, this article proposes an incursion into the empirical analysis of the interaction between companies' sustainable performance and stock market performance, focusing on the specificities of the Romanian financial market. It emphasizes the importance of a comprehensive approach that goes beyond simple financial figure analysis to include aspects such as sustainability, corporate governance, and social impact. The article aims to shed light on this complex relationship through rigorous empirical analysis applied to data specific to the Romanian market. We will thoroughly investigate the connections between companies' sustainability practices and the evolution of stock prices, taking into account the economic particularities of Romania, culminating with the estimation of a multiple linear regression model. Our study reveals that there is a correlation between the market capitalization of a company, its corporate performance and the specific industry or sector in which it operates.