Penalized Lq-likelihood estimators and variable selection in linear regression models

Abstract

Consider a linear regression model $$y_i=x_i^T\beta +e_i,i=1,2,\dots ,n,$$ where $\left\{e_i\right\}$ are independent identically distributed (iid) random variables with zero mean and known variance ${\sigma }^2.$ Based on the maximum Lq-likelihood estimator (MLqE) and the penalized likelihood estimator (PLE), we introduce a new parametric estimator which is called penalized Lq-likelihood estimator (PLqE). We investigate its Oracle properties and influence function. Simulation results support the validity of our approach. Furthermore, it is shown that the PLqE is robust, while the PLE is not.

Keywords:

• Linear regression models
• penalized Lq-likelihood estimators
• oracle properties
• influence function

MATHEMATICS SUBJECT CLASSIFICATION::

• 62J05

Additional information

Funding

This work was supported by National Natural Science Foundation of China (11471105).