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Strong approximation of multidimensional ℙ-ℙ plots processes by Gaussian processes with applications to statistical tests

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Abstract

The present paper is mainly concerned with the strong approximation of ℙ-ℙ plot processes in ℝd by sequences of Gaussian processes. In order to evaluate the limiting laws, a general notion of bootstrapped multidimensional ℙ-ℙ plots processes, constructed by exchangeably weighting sample, is presented and investigated. The applications discussed here are change-point detection in multivariate copula models and the law of iterated logarithm. Finally, we extend our framework to the K-sample problem and apply our results to derive the limiting laws of Kolmogorov-Smirnov and Cramér-von Mises statistics.

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  1. Labor. de Math. Appl., Univ. de Technol. de Compiegne, Compiegne, France

    S. Bouzebda

  2. Univ. Hassan II Mohammedia Casablanca, Mohammadia, Maroc

    T. Zari

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  1. S. Bouzebda
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  2. T. Zari
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Bouzebda, S., Zari, T. Strong approximation of multidimensional ℙ-ℙ plots processes by Gaussian processes with applications to statistical tests. Math. Meth. Stat. 23, 210–238 (2014). https://doi.org/10.3103/S1066530714030041

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