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About 6,912 papers for “regression coefficient estimation”

Coefficient regularizer based simultaneous regression estimation

Di‐Rong Chen, Heng Chen, Wei Huang · Scientia Sinica Mathematica · 2019

It is very important to extract the correlation between two random vectors $X$ and $Y$.The kernel method is used to extract nonlinear correlations.In this paper, the maximum correlation is obtained by minimizing variance ${\rm~Var}[f(X)-g(Y)]$, which is called simultaneous regression, where $f(X)$ and $g(Y)$ are respectively functions in two different reproducing kernel Hilbert spaces.We use regularized empirical variances minimization toconstruct estimates.In order to obtain the estimated function with sparsity,the $l_1$-norm of coefficient is used as the penalty term.We establish a learning rate under some mild conditions.Simultaneous regression is associated with canonical correlation analysis and slice inverse regression, etc.

Cited by 0Open access

Efficient estimation in varying coefficient regression models

Junfeng Huo, Xiuqing Zhou · Journal of Statistical Computation and Simulation · 2023

Varying coefficient models have been studied for many years, and local kernel estimation is an important method to estimate the coefficient functions. Since same bandwidth parameter is used for each coefficient function, local kernel estimation is not effective when the degree of smoothness is different for each coefficient function. In this paper, a new global estimation method based on kernel function and backfitting is proposed. In this method, different bandwidth parameters can be used for each coefficient function to improve the estimation accuracy, and asymptotic properties of the estimators are proved. To reduce the computational complexity, an adaptive global estimation method, which is based on an estimation of the bandwidth ratio and has only one bandwidth parameter to be selected, is proposed. Simulation results show that the proposed methods work well, and two real data examples further demonstrate the potential of the proposed methods.

Cited by 3

Dimension reduction and coefficient estimation in regression

Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 2018

991012655669103412 HKUST Electronic Theses Dimension reduction and coefficient estimation in regression by Linlin Dai thesis 2018 xiv, 119 pages : illustrations ; 30 cm In this thesis, we propose three novel dimension reduction and coefficient estimation methods for multivariate linear…Read more ›

Cited by 0

Dimension reduction and coefficient estimation in regression

Linlin Dai · 2018

991012655669103412 HKUST Electronic Theses Dimension reduction and coefficient estimation in regression by Linlin Dai thesis 2018 xiv, 119 pages : illustrations ; 30 cm In this thesis, we propose three novel dimension reduction and coefficient estimation methods for multivariate linear…Read more ›

Cited by 0

Estimation for time-varying coefficient smoothed quantile regression

Hu, Lixia, You, Jinhong, Huang, Qian et al. · Figshare · 2024

Time-varying coefficient regression is commonly used in the modeling of nonstationary stochastic processes. In this paper, we consider a time-varying coefficient <b>con</b>volution-type smoothed <b>qu</b>antil<b>e</b> <b>r</b>egression (<i>conquer</i>). The covariates and errors are assumed to belong to a general class of locally stationary processes. We propose a local linear <i>conquer</i> estimator for the varying-coefficient function, and obtain the global Bahadur–Kiefer representation, which yields the asymptotic normality. Furthermore, statistical inference on simultaneous confidence bands is also studied. We investigate the finite-sample performance of the <i>conquer</i> estimator and confirm the validity of our asymptotic theory by conducting extensive simulation studies. We also consider financial volatility data as an example of a real-world application.

Cited by 0Open access

On empirical Bayes estimation of multivariate regression coefficient

Rohana J. Karunamuni, Cheng Xiong · Greater South Information System · 2006

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression modelY=Xβ+ε, whereYis anm-vector of observations,Xis a knownm×kmatrix,βis an unknownk-vector, andεis anm-vector of unobservable random variables. The problem is squared error loss estimation ofβbased on some "previous" dataY1,…,Ynas well as the "current" data vectorYwhenβis distributed according to some unknown distributionG, whereYisatisfiesYi=Xβi+εi,i=1,…,n. We construct a new empirical Bayes estimator ofβwhenεi∼N(0,σ2Im),i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.

Cited by 0Open access

Minimum Distance Estimation in Random Coefficient Regression Models

Rudolf Beran, P. W. Millar · The Annals of Statistics · 1994

Random coefficient regression models are important in modeling heteroscedastic multivariate linear regression in econometrics. The analysis of panel data is one example. In statistics, the random and mixed effects models of ANOVA, deconvolution models and affine mixture models are all special cases of random coefficient regression. Some inferential problems, such as constructing prediction regions for the modeled response, require a good nonparametric estimator of the unknown coefficient distribution. This paper introduces and studies a consistent nonparametric minimum distance method for estimating the coefficient distribution. Our estimator translates the difficult problem of estimating an inverse Radon transform into a minimization problem.

Cited by 50Open access

On empirical Bayes estimation of multivariate regression coefficient

Rohana J. Karunamuni, Cheng Xiong · Greater South Information System · 2006

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression modelY=Xβ+ε, whereYis anm-vector of observations,Xis a knownm×kmatrix,βis an unknownk-vector, andεis anm-vector of unobservable random variables. The problem is squared error loss estimation ofβbased on some "previous" dataY1,…,Ynas well as the "current" data vectorYwhenβis distributed according to some unknown distributionG, whereYisatisfiesYi=Xβi+εi,i=1,…,n. We construct a new empirical Bayes estimator ofβwhenεi∼N(0,σ2Im),i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.

Cited by 0Open access

Reduced-rank clustered coefficient regression for addressing multicollinearity in heterogeneous coefficient estimation

Yan Zhong, Kejun He, Gefei Li · Biometrics · 2024

Clustered coefficient regression (CCR) extends the classical regression model by allowing regression coefficients varying across observations and forming clusters of observations. It has become an increasingly useful tool for modeling the heterogeneous relationship between the predictor and response variables. A typical issue of existing CCR methods is that the estimation and clustering results can be unstable in the presence of multicollinearity. To address the instability issue, this paper introduces a low-rank structure of the CCR coefficient matrix and proposes a penalized non-convex optimization problem with an adaptive group fusion-type penalty tailor-made for this structure. An iterative algorithm is developed to solve this non-convex optimization problem with guaranteed convergence. An upper bound for the coefficient estimation error is also obtained to show the statistical property of the estimator. Empirical studies on both simulated datasets and a COVID-19 mortality rate dataset demonstrate the superiority of the proposed method to existing methods.

Cited by 3

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

Sévérien Nkurunziza, S. Ejaz Ahmed · Statistica Neerlandica · 2011

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.

Cited by 19