A randomly swapped bootstrap for paired data: testing equality of distribution for correlated samples

Wei Siang Wang (), Christine Amsler () and Peter Schmidt ()
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Wei Siang Wang: Nanyang Technological University
Christine Amsler: Michigan State University
Peter Schmidt: Michigan State University

Empirical Economics, 2025, vol. 69, issue 5, No 4, 2609-2626

Abstract: Abstract We consider tests of the hypothesis that two random variables $$X$$ X and $$Y$$ Y have the same distribution. Standard tests of this hypothesis, like the Kolmogorov–Smirnov two-sample test and the Baumgartner–Weiss–Schindler test, assume that $$X$$ X and $$Y$$ Y are independent, and we do not assume this. Instead we suppose that our sample consists of observations on pairs $${({x}_{i},{y}_{i})}_{i=1}^{n}$$ ( x i , y i ) i = 1 n , where we have random sampling (therefore independence) over $$i$$ i , but unrestricted dependence between $$X$$ X and $$Y$$ Y . We provide a novel form of the bootstrap that provides asymptotically valid critical values for the Kolmogorov–Smirnov two-sample test and the Baumgartner–Weiss–Schindler test. We conduct some Monte Carlo simulations to assess the finite-sample properties of these tests.

Keywords: Bootstrap; Paired data; Test of equality of distributions; Kolmogorov–Smirnov two-sample test (search for similar items in EconPapers)
JEL-codes: C10 C15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00181-025-02779-0

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