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Statistical Decision Theory and Related Topics V pp 1–18Cite as

Minimaxity, More or Less

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Abstract

This is a historical study of the minimax idea in statistics and of its creator, Abraham Wald. The focus is on the place of minimaxity in the development of statistics over the last half century.

In formal terms minimaxity is an objective criterion which severely restricts the class of acceptable statistical decision procedures. However, this was not how Wald and his close collaborators came to view it, nor has it proved to serve this function. Rather, minimaxity has been a vital organizing theme in many areas of statistics.

Following the brief historical study of Wald himself and of his development of the minimax idea we look at some of the statistical problems in which minimaxity has played a key role as an organizing theme. These areas include asymptotic statistical theory, the Fibonacci search algorithm, robust Bayes analysis, robust estimation, optimum design, and nonparametric function estimation.

Informal discussion with many colleagues has provided helpful input to this study. I particularly want to thank Jim Berger, Peter Bickel and David Siegmund.

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Authors and Affiliations

  1. Cornell University, USA

    Lawrence D. Brown

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  1. Lawrence D. Brown
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Editor information

Editors and Affiliations

  1. Department of Statistics, Purdue University, 47907, West Lafayette, IN, USA

    Shanti S. Gupta  & James O. Berger  & 

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© 1994 Springer-Verlag New York, Inc.

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Brown, L.D. (1994). Minimaxity, More or Less. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics V. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2618-5_1

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  • DOI: https://doi.org/10.1007/978-1-4612-2618-5_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7609-8

  • Online ISBN: 978-1-4612-2618-5

  • eBook Packages: Springer Book Archive

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