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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.
"synopsis" may belong to another edition of this title.
About the Author
Marvin H. J. Gruber is a professor of mathematics and statistics at the Rochester Institute of Technology.
Review
"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"About this title" may belong to another edition of this title.
- PublisherJohns Hopkins University Press
- Publication date2010
- ISBN 10 0801894263
- ISBN 13 9780801894268
- BindingHardcover
- LanguageEnglish
- Edition number2
- Number of pages424
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Mathematical works printed in the Americas, 1554-1700.
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Condition: as new. Baltimore, Md. : Johns Hopkins University Press, 2009. Hardcover. xi,373 pp. - This magisterial annotated bibliography of the earliest mathematical works to be printed in the New World challenges long-held assumptions about the earliest examples of American mathematical endeavor. Bruce Stanley Burdick brings together mathematical writings from Mexico, Lima, and the English colonies of Massachusetts, Pennsylvania, and New York. The book provides important information such as author, printer, place of publication, and location of original copies of each of the works discussed. Burdick's exhaustive research has unearthed numerous examples of books not previously cataloged as mathematical. While it was thought that no mathematical writings in English were printed in the Americas before 1703, Burdick gives scholars one of their first chances to discover Jacob Taylor's 1697 Tenebrae, a treatise on solving triangles and other figures using basic trigonometry. He also goes beyond the English language to discuss works in Spanish and Latin, such as Alonso de la Vera Cruz's 1554 logic text, the Recognitio Summularum; a book on astrology by Enrico Martinez; books on the nature of comets by Carlos de Siguenza y Gongora and Eusebio Francisco Kino; and a 1676 almanac by Feliciana Ruiz, the first woman to produce a mathematical work in the Americas. Those fascinated by mathematics, its history, and its culture will note with interest that many of these works, including all of the earliest ones, are from Mexico, not from what is now the United States. As such, the book will challenge us to rethink the history of mathematics on the American continents. Condition : as new copy. ISBN 9780801894268. Keywords : MATHEMATICS, bibliography. Seller Inventory # 284530
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Regression estimators : a comparative study.
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Condition: as new. 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
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