Regression estimators : a comparative study.

Gruber, Marvin H.J.

ISBN 10: 0801894263 / ISBN 13: 9780801894268

Published by Johns Hopkins University Press, 2010

About this Item

Baltimore, Md. : Johns Hopkins University Press, 2010. Hardcover. xii,412 pp. - 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. Condition : as new copy. ISBN 9780801894268. Keywords : MATHEMATICS,

Seller Inventory # 284529

Bibliographic Details

• Title: Regression estimators : a comparative study.
• Publisher: Johns Hopkins University Press
• Publication Date: 2010
• Language: English
• ISBN 10: 0801894263
• ISBN 13: 9780801894268
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: as new

About this title

Synopsis

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.