Variable Selection in Restricted Linear Regression Models

TL;DR

This paper explores variable selection and parameter estimation in restricted linear regression models using the LASSO method, demonstrating its effectiveness through simulations and real data applications.

Contribution

It introduces the application of LASSO for variable selection in non-stochastic restricted linear regression models, combining prior information with modern regularization techniques.

Findings

LASSO effectively selects variables in restricted regression models.

Simulation results show improved estimation accuracy.

Real data example confirms practical utility.

Abstract

The use of prior information in the linear regression is well known to provide more efficient estimators of regression coefficients. The methods of non-stochastic restricted regression estimation proposed by Theil and Goldberger (1961) are preferred when prior information is available. In this study, we will consider parameter estimation and the variable selection in non-stochastic restricted linear regression model, using least absolute shrinkage and selection operator (LASSO) method introduced by Tibshirani (1996). A small simulation study and real data example are provided to illustrate the performance of the proposed method for dealing with the variable selection and the parameter estimation in restricted linear regression models.