Nonparametric changepoint procedures for repeated measures data

Abstract

Let (X_i1,…,X_in), i = 1,…, m, be m mutually independent, identically distributed, continuous n-dimensional random vectors. The setting where (X_i1,…,X_ir) is an exchangeable vector and (X_i,r+1,…,X_in) is an exchangeable vector but the complete vector (X_i1,…,X_in) is not exchangeable for i = 1, 2,…, m, and some unknown integer r, l < r < n - l, is referred to as a changepoint problem for repeated measures data with at most one change. In this paper we propose three nonparametric procedures to test for non-exchangeability in such data resulting from a change in location. Simulated small-sample null distributions for the three test statistics are obtained and asymptotic approximations for those null distributions are provided. When a change is detected to be significant by one or more of these tests, estimators for the changepoint r and the magnitude of the change are proposed and studied.

Keywords:

• Changepoint
• Repeated Measures
• Mann-Whitney-Wilcoxon Statistic
• U-statistics

^∗This work was supported in part by the Office of Naval Research through Contract No. N00014–84-K-0422 and formed a part of the first author’s Ph.D. Dissertation at The Ohio State University.

^∗This work was supported in part by the Office of Naval Research through Contract No. N00014–84-K-0422 and formed a part of the first author’s Ph.D. Dissertation at The Ohio State University.

Notes

^∗This work was supported in part by the Office of Naval Research through Contract No. N00014–84-K-0422 and formed a part of the first author’s Ph.D. Dissertation at The Ohio State University.