The Annals of Statistics

Bahadur Efficiency of Rank Tests for the Change-Point Problem

Jaap Praagman

Abstract

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.

Article information

Source
Ann. Statist., Volume 16, Number 1 (1988), 198-217.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350700

Digital Object Identifier
doi:10.1214/aos/1176350700

Mathematical Reviews number (MathSciNet)
MR924866

Zentralblatt MATH identifier
0668.62028

JSTOR