The Annals of Statistics

Cell Selection in the Chernoff-Lehmann Chi-Square Statistic

M. C. Spruill

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 375-383.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343413

Digital Object Identifier
doi:10.1214/aos/1176343413

Mathematical Reviews number (MathSciNet)
MR391379

Zentralblatt MATH identifier
0326.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62F10: Point estimation

Keywords
Chi-square test Bahadur slope

Citation

Spruill, M. C. Cell Selection in the Chernoff-Lehmann Chi-Square Statistic. Ann. Statist. 4 (1976), no. 2, 375--383. doi:10.1214/aos/1176343413. https://projecteuclid.org/euclid.aos/1176343413


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