Theory of Ridge Regression Estimators with Applica tions, Saleh

This book discusses current methods of estimation in linearmodels. In particular, the authors address the methodology oflinear multiple regression models that plays an important role inalmost every scientific investigations in various fields, including economics, engineering, and biostatistics. Thestandard estimation method for regression parameters is theordinary least square (OLS) principal where residual squared errorsare minimized. Applied statisticians are often not satisfied withOLS estimators when the design matrix is ill-conditioned, leadingto a multicollinearity problem and large variances that make theprediction inaccurate. This book details theridge regression estimator, which was developed to combat themulticollinearity problem. Another estimator, called theLiu-estimator due to Liu Kejian, is also addressed since itprovides a competing resolution to the multicollinearityproblem. The ridge regression estimators are complicatednon-linear functions of the ridge parameter, whereas, theLiu estimators are a linear function of the shrinkage parameter.With a focus on the ridge regression and LIU estimators, this bookprovides expanded coverage beyond the usual preliminary test andStein type estimator. In this case, we propose a class of compositeestimators that are obtained by multiplying the OLS, restrictedOLS, preliminary test OLS, and Stein-type OLS by the ridgefactor and Liu-factor. This research is asignificant step towards the study of dominance properties as wellas the comparison of the extent of LASSO properties. In addition, research materials involving shrinkage and model selection forlinear regression models are provided. Topical coverageincludes: preliminaries; linear regression models; multipleregression models; measurement error models; generalized linearmodels; and autoregressive Gaussian processes.