Some Non-asymptotic Rank Tests for Change Points in Regression

Silvelyn Zwanzig () and Rauf Ahmad ()
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Silvelyn Zwanzig: Uppsala University, Department of Mathematics
Rauf Ahmad: Uppsala University, Department of Statistics

Chapter Chapter 13 in Asymptotic and Methodological Statistics, 2026, pp 257-274 from Springer

Abstract: Abstract Rank-based tests for detecting the presence of change point in a linear regression model are presented. We build upon Theil’s idea, namely to consider the slope of all connecting lines, instead of the original points. We, however, use the idea to construct change point rank tests in regression in a way that it reduces the problem to a two-sample problem. Wilcoxon type tests are proposed, with ranks assigned to the pooled sample, whose exact distribution is known under the null hypothesis of no change point. Simple linear regression models are considered, for both fixed and random design. Extensions to multivariate and errors-in-variables models are discussed.

Date: 2026
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DOI: 10.1007/978-3-032-07178-1_13

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