## The Annals of Statistics

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

### Bahadur Efficiency of Rank Tests for the Change-Point Problem

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62G20: Asymptotic properties

Secondary: 62G10: Hypothesis testing

**Keywords**

Bahadur efficiency linear rank test change-point test

#### Citation

Praagman, Jaap. Bahadur Efficiency of Rank Tests for the Change-Point Problem. Ann. Statist. 16 (1988), no. 1, 198--217. doi:10.1214/aos/1176350700. https://projecteuclid.org/euclid.aos/1176350700