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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Bibliographic Details
Published in:Mathematical methods of statistics Vol. 23; no. 3; pp. 210 - 238
Main Authors: Bouzebda, S., Zari, T.
Format: Journal Article
Language:English
Published: Heidelberg Allerton Press 01.07.2014
Springer
Subjects:
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
Online Access:Get full text
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Summary: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