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March, 1988 Bahadur Efficiency of Rank Tests for the Change-Point Problem
Jaap Praagman
Ann. Statist. 16(1): 198-217 (March, 1988). DOI: 10.1214/aos/1176350700


A sequence of independent random variables $X_1, X_2, \cdots, X_N$ is said to have a change point if $X_1, X_2, \cdots, X_n$ have a common distribution $F$ and $X_{n+1}, \cdots, X_N$ have a common distribution $G, G \neq F$. Consider the problem of testing the null hypothesis of no change against the alternative of a change $G < F$ at an unknown change point $n$. Two classes of statistics based upon two-sample linear rank statistics (max- and sum-type) are compared in terms of their Bahadur efficiency. It is shown that for every sequence of sum-type statistics a sequence of max-type statistics can be constructed with at least the same Bahadur slope at all possible alternatives. Special attention is paid to alternatives close to the null hypothesis.


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Jaap Praagman. "Bahadur Efficiency of Rank Tests for the Change-Point Problem." Ann. Statist. 16 (1) 198 - 217, March, 1988.


Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0668.62028
MathSciNet: MR924866
Digital Object Identifier: 10.1214/aos/1176350700

Primary: 62G20
Secondary: 62G10

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • March, 1988
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