Regression Estimators: A Comparitive Study.

Gruber, Marvin H. J.

Picture of Regression Estimators: A Comparitive Study.
I’m not at all sure I can explain this properly, although it looks as if it wold be helpful for graduate students and professional statisticians. It ‘…summarises basic ideas in matrix theory and statistical decision theory, and explores the mathematical relationships between estimators from both Bayesian and Frequentist points of view. It considers the efficiency of estimators with and without averaging over a prior distribution, and applies all this to the Kalman Filter, analysis of variance models, and penalized splines.‘ And more. Scholarly stuff.

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SKU: 9780801894268


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.

Book Details

Author Gruber, Marvin H. J.
Format HC
Publisher John Hopkins
Publish Date 0/01/1900
Catalogue Aug18
Catalogue book number 210