Cramér‐von Mises tests for change points. (8th July 2021)

• Record Type: Journal Article
• Authors: Erlemann, Rasmus; Lockhart, Richard; Yao, Rihan
• Is Part Of: Scandinavian journal of statistics. Volume 49:Number 2(2022)
• Page Start: 802
• Page End: 830
• Publication Date: 2021-07-08
• Subjects: asymptotic distribution -- change point detection -- Cramér–von Mises two‐sample test -- Monte Carlo simulation -- nonparametric test statistics; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12544
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramér–von Mises two‐sample test computed at every possible change point. One test uses the largest such test statistic over all possible change points; the other averages over all possible change points. Large sample theory for the average statistic is shown to provide useful p ‐values much more quickly than bootstrapping, particularly in long sequences. Power is analyzed for contiguous alternatives. The average statistic is shown to have limiting power larger than its level for such alternative sequences. Evidence is presented that this is not true for the maximal statistic. Asymptotic methods and bootstrapping are used for constructing the test distribution. Performance of the tests is checked with a Monte Carlo power study for various alternative distributions.