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

Consider a linear regression model yi = x(i)(T) beta + e(i), i = 1,2,..., n, where {e(i)} 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.