Distribution-Free Tests for the Changepoint Problem

SYNOPTIC ABSTRACT

Let X₁, X₂, …, X_r+1, …, X_n be independent, continuous random variables such that X_i, i = l, …, r, has an unknown distribution function F(x), and X_j, j = r + 1, …, n, has distribution function F(x - Θ), with Θ unknown (−∞ < Θ < ∞). The integer r, which is called the changepoint, is also taken to be unknown. The hypothesis to be tested is H₀ : Θ = 0 (i.e., no change) vs. either one- or two-sided alternatives. We consider distribution-free tests for this problem based on Mann-Whitney-Wilcoxon statistics, and study their large sample properties. We also report on some Monte Carlo power comparisons involving these procedures and several parametric competitors.

Key Words and Phrases:

• Changepoint problem
• distribution-free tests
• approximations to null distributions
• Monte Carlo power study
• Gaussian processes