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Nonparametric comparison of several transformations of distribution functions

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  • Mohamed Boutahar
  • Badih Ghattas
  • Denys Pommeret

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.

Suggested Citation

  • Mohamed Boutahar & Badih Ghattas & Denys Pommeret, 2013. "Nonparametric comparison of several transformations of distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 619-633, September.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:619-633
    DOI: 10.1080/10485252.2013.799158
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