scholarly journals Bayesian Variable Selection in Linear Regression Models with Inequality Constraints on the Coefficients

2002 ◽  
Vol 15 (1) ◽  
pp. 73-84
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Inequality Constraints ◽  
Bayesian Variable Selection ◽  
Linear Regression Models

scholarly journals Bayesian variable selection in linear regression models with non-normal errors

2018 ◽  
Vol 28 (2) ◽  
pp. 323-358 ◽  
Author(s):  
Saverio Ranciati ◽  
Giuliano Galimberti ◽  
Gabriele Soffritti
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Linear Regression Models

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

scholarly journals Stochastic Restricted LASSO-Type Estimator in the Linear Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Manickavasagar Kayanan ◽  
Pushpakanthie Wijekoon
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Prior Information ◽  
Estimation Procedure ◽  
Regression Coefficients ◽  
Linear Regression Models ◽  
Monte Carlo Simulation Study ◽  
Regression Parameters ◽  
Linear Restrictions

Among several variable selection methods, LASSO is the most desirable estimation procedure for handling regularization and variable selection simultaneously in the high-dimensional linear regression models when multicollinearity exists among the predictor variables. Since LASSO is unstable under high multicollinearity, the elastic-net (Enet) estimator has been used to overcome this issue. According to the literature, the estimation of regression parameters can be improved by adding prior information about regression coefficients to the model, which is available in the form of exact or stochastic linear restrictions. In this article, we proposed a stochastic restricted LASSO-type estimator (SRLASSO) by incorporating stochastic linear restrictions. Furthermore, we compared the performance of SRLASSO with LASSO and Enet in root mean square error (RMSE) criterion and mean absolute prediction error (MAPE) criterion based on a Monte Carlo simulation study. Finally, a real-world example was used to demonstrate the performance of SRLASSO.

scholarly journals A One-Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models

2016 ◽  
Vol 2016 (290) ◽  
Author(s):  
Alexander Chudik ◽  
◽  
George Kapetanios ◽  
M. Hashem Pesaran ◽  
◽  
...  
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Multiple Testing ◽  
High Dimensional ◽  
Linear Regression Models ◽  
Testing Approach

Variable selection via generalized SELO-penalized linear regression models

2018 ◽  
Vol 33 (2) ◽  
pp. 145-162 ◽  
Author(s):  
Yue-yong Shi ◽  
Yong-xiu Cao ◽  
Ji-chang Yu ◽  
Yu-ling Jiao
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Linear Regression Models
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