Ridge Regression in Theory and Applications
A. K. Md. Ehsanes Saleh, Mohammad Arashi, B. M. Golam Kibria · Wiley series in probability and statistics · 2019
The multiple linear regression model is one of the best known and widely used among the models for statistical data analysis in every field of sciences and engineering as well as in social sciences, economics, and finance. This chapter is concerned with the study of the rigid regression estimator (RRE) for the regression coefficients and its characteristic properties, and compares its relation with the least absolute shrinkage and selection operator (LASSO). It considers the preliminary test estimator (PTE) and the Stein-type ridge estimator in low dimension, and studies their dominance properties. The chapter discusses the asymptotic distributional theory of the ridge estimators following Knight and Fu. Ridge trace is a diagnostic test that gives a readily interpretable picture of the effects of nonorthogonality and may guide to a better point estimate. The optimization algorithm for estimating the LASSO estimator is discussed, and prostate cancer data are used to illustrate the optimization algorithm.