Choice of Smoothing Parameter for Kernel Type Ridge Estimators in Semiparametric Regression Models

Abstract

This paper concerns kernel-type ridge estimators of parameters in a semiparametric model. These estimators are a generalization of the well-known Speckman’s approach based on kernel smoothing method. The most important factor in achieving this smoothing method is the selection of the smoothing parameter. In the literature, many selection criteria for comparing regression models have been produced. We will focus on six selection criterion improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), Mallows’ Cp criterion, risk estimation using classical pilots (RECP), Bayes information criterion (BIC), and restricted maximum likelihood (REML). Real and simulated data sets are considered to illustrate the key ideas in the paper. Thus, suitable selection criterion are provided for optimum smoothing parameter selection.

Keywords

• semiparametric model
• kernel smoothing
• ridge type estimator
• smoothing parameter generalized cross-validation