The Annals of Statistics

Adaptive Procedures in Multiple Decision Problems and Hypothesis Testing

Andrew L. Rukhin

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Abstract

Necessary and sufficient conditions for the existence of adaptive procedures for identification of one of several probability distributions or for testing a simple hypothesis against a simple alternative are obtained. By definition, adaptive procedures are required to exhibit the same asymptotic behavior for several parametric families as do the optimal (minimax) estimators for each of these families. The proofs are based on a multivariate version of Chernoff's theorem, providing asymptotic formulas for probabilities of large deviations for sums of i.i.d. random vectors. Some examples of adaptive procedures are considered, and the non-existence of such rules is established in certain situations.

Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1148-1162.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345980

Digital Object Identifier
doi:10.1214/aos/1176345980

Mathematical Reviews number (MathSciNet)
MR673650

Zentralblatt MATH identifier
0512.62046

JSTOR
links.jstor.org

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62F12: Asymptotic properties of estimators 62F05: Asymptotic properties of tests 60F10: Large deviations

Keywords
Multiple decision problem with finite parameter space testing of simple hypothesis probability of incorrect decision adaptive procedures multivariate Chernoff's theorem

Citation

Rukhin, Andrew L. Adaptive Procedures in Multiple Decision Problems and Hypothesis Testing. Ann. Statist. 10 (1982), no. 4, 1148--1162. doi:10.1214/aos/1176345980. https://projecteuclid.org/euclid.aos/1176345980


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