Theory of Ridge Regression Estimation with Applications

1Introduction to Ridge Regression

This chapter reviews the developments of ridge regression, starting with the definition of ridge regression together with the covariance matrix. We discuss the multicollinearity problem and ridge notion and present the preliminary test and Stein‐type estimators. In addition, we discuss the high‐dimensional problem. In conclusion, we include detailed notes, references, and organization of the book.

1.1 Introduction

Consider the common multiple linear regression model with the vector of coefficients, given by

(1.1)

where is a vector of responses, is an design matrix of rank , is the vector of covariates, and is an ‐vector of independently and identically ...