Open Access
March, 1982 Asymptotic Lognormality of $P$-Values
Diane Lambert, W. J. Hall
Ann. Statist. 10(1): 44-64 (March, 1982). DOI: 10.1214/aos/1176345689


Sufficient conditions for asymptotic lognormality of exact and approximate, unconditional and conditional $P$-values are established. It is pointed out that the mean, which is half the Bahadur slope, and the standard deviation of the asymptotic distribution of the log transformed $P$-value together, but not the mean alone, permit approximation of both the level and power of the test. This provides a method of discriminating between tests that have Bahadur efficiency one. The asymptotic distributions of the log transformed $P$-values of the common one- and two-sample tests for location are derived and compared.


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Diane Lambert. W. J. Hall. "Asymptotic Lognormality of $P$-Values." Ann. Statist. 10 (1) 44 - 64, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0484.62038
MathSciNet: MR642718
Digital Object Identifier: 10.1214/aos/1176345689

Primary: 62F20
Secondary: 62G20

Keywords: $p$-value , Bahadur efficiency , one-sample tests , slope , two-sample tests

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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