Nonparametric comparison of several transformations of distribution functions

Mohamed Boutahar, Badih Ghattas and Denys Pommeret

Journal of Nonparametric Statistics, 2013, vol. 25, issue 3, 619-633

Abstract: This paper considers two random variables such that there exists a monotone transformation between their distribution functions. The problem is to test if there is a change in this transformation when these two variables are observed under K different conditions. The approach considered is a CUSUM test based on the cumulative sum of the residuals and a test statistic is proposed for testing the equality of the K transformations. The asymptotic distribution of the test statistic is derived and its finite sample properties are examined by simulation. As a further illustration, an analysis of a real data set concerning the impact of the financial crisis of September 2008 is given.

Date: 2013
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DOI: 10.1080/10485252.2013.799158

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