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

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 present...

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Vydáno v:Mathematical methods of statistics Ročník 23; číslo 3; s. 210 - 238
Hlavní autoři: Bouzebda, S., Zari, T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Allerton Press 01.07.2014
Springer
Témata:
Functional Analysis
Mathematics
Mathematics and Statistics
Probability
Statistical Theory and Methods
Statistics
Statistics Theory
strong invariance principles
secondary 62G07, 62G10
exchangeable bootstrap
dependence function
primary 60F05, 60F15, 60E05, 62G30, 60F17
Gaussian processes
empirical and quantile processes
weak convergence
ℙ-ℙ plots
change-point
K-sample problem
ISSN:1066-5307, 1934-8045
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Shrnutí: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.
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530714030041