Theory of Ridge Regression Estimation with Applications

7Partially Linear Regression Models

7.1 Introduction

In this chapter, the problem of ridge estimation is studied in the context of partially linear models (PLMs). In a nutshell, PLMs are smoothed models that include both parametric and nonparametric parts. They allow more flexibility compared to full/nonparametric regression models.

Consider the usual PLM with the form

(7.1)

where is a vector of explanatory variables, is an unknown ‐dimensional parameter vector, the 's are known and nonrandom in some bounded domain , is an unknown smooth function, and 's are i.i.d. random errors with mean 0, variance , which are independent of . PLMs are more flexible than standard linear models since they ...