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March, 1976 Cell Selection in the Chernoff-Lehmann Chi-Square Statistic
M. C. Spruill
Ann. Statist. 4(2): 375-383 (March, 1976). DOI: 10.1214/aos/1176343413


The approximate Bahadur slope of the Chernoff-Lehmann $\chi^2$-test-of-fit to a scale-location family on $R^k$ is computed. The goal is to select cells (whose number is independent of sample size) to maximize this slope. The supremum is found and is shown to be a maximum only in trivial cases. If the $\sup$ is finite there is always a best selection for a fixed number of cells. Equally likely cells are shown to be admissible when the alternative is large.


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M. C. Spruill. "Cell Selection in the Chernoff-Lehmann Chi-Square Statistic." Ann. Statist. 4 (2) 375 - 383, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0326.62035
MathSciNet: MR391379
Digital Object Identifier: 10.1214/aos/1176343413

Primary: 62G20
Secondary: 62F10

Keywords: Bahadur slope , Chi-square test

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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