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Regression Estimators: A Comparative Study
Contributor(s): Gruber, Marvin H. J. (Author)
ISBN: 0801894263     ISBN-13: 9780801894268
Publisher: Johns Hopkins University Press
OUR PRICE:   $115.90  
Product Type: Hardcover
Published: June 2010
Qty:
Temporarily out of stock - Will ship within 2 to 5 weeks
Additional Information
BISAC Categories:
- Mathematics | Probability & Statistics - Regression Analysis
- Mathematics | Applied
Dewey: 519.544
LCCN: 2009024466
Physical Information: 1.1" H x 6.2" W x 9" (1.50 lbs) 424 pages
 
Descriptions, Reviews, Etc.
Publisher Description:

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.


Contributor Bio(s): Gruber, Marvin H. J.: - Marvin H. J. Gruber is a professor of mathematics and statistics at the Rochester Institute of Technology.