The consistency of a matching test

Let X ∗ 1⩽X ∗ 2⩽⋯⩽X ∗ n be the order statistics of a random sample from a distribution on [0, 1]. Let A k , the kth match, be the event that X ∗ kϵ( (k−1) n k n ], and let S n be the total number of matches. The consistency of S n for testing uniform df, U, against df G≠ U is investigated, and it is...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1982, Vol.6 (3), p.227-233
Main Author: Siddiqui, M.M.
Format: Article
Language:English
Subjects:
Consistency
Matching
Order Statistics
Test
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Summary:Let X ∗ 1⩽X ∗ 2⩽⋯⩽X ∗ n be the order statistics of a random sample from a distribution on [0, 1]. Let A k , the kth match, be the event that X ∗ kϵ( (k−1) n k n ], and let S n be the total number of matches. The consistency of S n for testing uniform df, U, against df G≠ U is investigated, and it is shown that S n is consistent if the intersection of G with U has Lebesgue measure zero. It is also consistent against a sequence of alternatives approaching U at a rate less faster than n -1 2 .
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(82)90027-1