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June, 1991 Sensitive and Sturdy $p$-Values
John I. Marden
Ann. Statist. 19(2): 918-934 (June, 1991). DOI: 10.1214/aos/1176348128


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.


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John I. Marden. "Sensitive and Sturdy $p$-Values." Ann. Statist. 19 (2) 918 - 934, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62016
MathSciNet: MR1105852
Digital Object Identifier: 10.1214/aos/1176348128

Primary: 62F03
Secondary: 62C15 , 62C20 , 62F04 , 62H15

Keywords: $P$-values , Bartlett's problem , exponential family , Fisher's procedure , Hypothesis tests , Meta-analysis , normal distribution , Outliers , robustness , spherical symmetry

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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