Strong approximation of multidimensional ℙ-ℙ plots processes by Gaussian processes with applications to statistical tests - Bouzebda, S.; Zari, T. (Mathematical methods of statistics, 2014)
The present paper is mainly concerned with the strong approximation of ℙ-ℙ plot processes in ℝ d 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.