On powerful distributional tests based on sample spacings
This paper is devoted to tests for uniformity based on sum-functions of m-spacings, where m diverges to infinity as the sample size, n, increases. It is shown that if m diverges at a slower rate than n1/2 then the commonly used sum-function will detect alternatives distant (mn)-1/4 from the uniform. This result fails if m diverges more quickly than n1/2, and in that situation the statistic must be modified. The case where m/n --> [varrho], 0 < [varrho] < 1, is also considered, and it is shown that the test has adequate power against local and fixed alternatives if and only if [varrho] is irrational.
Year of publication: |
1986
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---|---|
Authors: | Hall, Peter |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 19.1986, 2, p. 201-224
|
Publisher: |
Elsevier |
Keywords: | central limit theorem fixed alternative local alternative order statistic power spacings test uniform distribution |
Saved in:
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