Open Access
Translator Disclaimer
October, 1995 Nonparametric Tests for Nonstandard Change-Point Problems
D. Ferger
Ann. Statist. 23(5): 1848-1861 (October, 1995). DOI: 10.1214/aos/1176324326


We consider independent random elements $X_1, \ldots, X_n, n \in \mathbb{N}$, with values in a measurable space $(\mathscr{X}, \mathscr{B})$ so that $X_1, \ldots, X_{\lbrack n\theta\rbrack}$ have a common distribution $\nu_1$ and the remaining $X_{\lbrack n\theta\rbrack + 1}, \ldots, X_n$ have a common distribution $\nu_2 \neq \nu_1$, for some $\theta \in (0, 1)$. The change point $\theta$ as well as the distributions are unknown. A family of tests is introduced for the nonstandard change-point problem $H_0: \theta \in \Theta_0$ versus $H_1: \theta \not\in \Theta_0$, where $\Theta_0$ is an arbitrary subset of (0, 1). The tests are shown to be asymptotic level-$\alpha$ tests and to be consistent on a large class of alternatives. The same holds for the corresponding bootstrap versions of the tests. Moreover, we present a detailed investigation of the local power.


Download Citation

D. Ferger. "Nonparametric Tests for Nonstandard Change-Point Problems." Ann. Statist. 23 (5) 1848 - 1861, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62054
MathSciNet: MR1370310
Digital Object Identifier: 10.1214/aos/1176324326

Primary: 62G10
Secondary: 60F05 , 62G09 , 62G20

Keywords: bootstrap , consistency , local power , maximizer of a two-sided random walk , Tests for change-point problems

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 5 • October, 1995
Back to Top