The Annals of Statistics

Sensitive and Sturdy $p$-Values

John I. Marden

Full-text: Open access

Abstract

We introduce new criteria for evaluating test statistics based on the $p$-values of the statistics. Given a set of test statistics, a good statistic is one which is robust in being reasonably sensitive to all departures from the null implied by that set. We present a constructive approach to finding the optimal statistic. We apply the criteria to two-sided problems; combining independent tests; testing that the mean of a spherical normal distribution is 0, and extensions to other spherically symmetric and exponential distributions; Bartlett's problem of testing the equality of several normal variances; and testing for one outlier in a normal linear model. For the most part, the optimal statistic is quite easy to use. Often, but not always, it is the likelihood ratio statistic.

Article information

Source
Ann. Statist. Volume 19, Number 2 (1991), 918-934.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176348128

Digital Object Identifier
doi:10.1214/aos/1176348128

Mathematical Reviews number (MathSciNet)
MR1105852

Zentralblatt MATH identifier
0729.62016

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62C20: Minimax procedures 62F04 62H15: Hypothesis testing 62C15: Admissibility

Keywords
Hypothesis tests $p$-values robustness meta-analysis Fisher's procedure normal distribution spherical symmetry exponential family outliers Bartlett's problem

Citation

Marden, John I. Sensitive and Sturdy $p$-Values. Ann. Statist. 19 (1991), no. 2, 918--934. doi:10.1214/aos/1176348128. http://projecteuclid.org/euclid.aos/1176348128.


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