Robust penalized empirical likelihood estimation method for linear regression

Abstract

Maximum likelihood estimation is a popular method for parameter estimation in regression models. However, since in some data sets it may not be possible to make any distributional assumptions on the error term, the likelihood method cannot be used to estimate the parameters of interest. For those data sets, one can use the empirical likelihood estimation method to estimate the parameters of a linear regression model. The aim of this study is to propose a robust penalized empirical likelihood estimation method to estimate the regression parameters and select significant variables, simultaneously, for data scenarios for which a well-defined likelihood function may not be available. This will be achieved by combining a robust empirical estimation method and the bridge penalty function. We investigate the asymptotic properties of the proposed estimator and explore the finite sample behaviour with a simulation study and a real data example.