An examination of mathematical formulations of ridge-regression-type estimators points to a curious observation: estimators can be derived by both Bayesian and Frequentist methods. In this updated and expanded edition of his 1990 treatise on the subject, Marvin H. J. Gruber presents, compares, and contrasts the development and properties of ridge-type estimators from these two philosophically different points of view. The book is organized into five sections. Part I gives a historical survey of the literature and summarizes basic ideas in matrix theory and statistical decision theory. Part II explores the mathematical relationships between estimators from both Bayesian and Frequentist points of view. Part III considers the efficiency of estimators with and without averaging over a prior distribution. Part IV applies the methods and results discussed in the previous two sections to the Kalman Filter, analysis of variance models, and penalized splines. Part V surveys recent developments in the field. These include efficiencies of ridge-type estimators for loss functions other than squared error loss functions and applications to information geometry. Gruber also includes an updated historical survey and bibliography. With more than 150 exercises, Regression Estimators is a valuable resource for graduate students and professional statisticians.

About the Author
Marvin H. J. Gruber is a professor of mathematics and statistics at the Rochester Institute of Technology.

Reviews
"A comprehensive treatment... valuable to statisticians who would like to know more about the analytical properties of ridge-type estimators." - Journal of the American Statistical Association "Highly recommended to anyone working on advanced applications or research in estimation in linear models." - Technometrics"



Book Information
ISBN 9780801894268
Author Marvin H. J. Gruber
Format Hardback
Page Count 424
Imprint Johns Hopkins University Press
Publisher Johns Hopkins University Press
Weight(grams) 680g
Dimensions(mm) 229mm * 152mm * 29mm