Afrika Statistika

Weighted multivariate Cramér-von Mises-type statistics

Paul Deheuvels

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In this paper, we consider weighted quadratic functionals of the multivariate uniform empirical process. By deriving the Karhunen-Loève expansion of the corresponding limiting Gaussian process, we obtain the asymptotic distribution of these statistics. Our results have direct applications to tests of goodness of fit and tests of independence by Cramér-von Mises-type statistics.

Article information

Afr. Stat. Volume 1, Number 1 (2005), 1-14.

Received: 28 February 2005
First available in Project Euclid: 26 May 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 60G15: Gaussian processes 62E20: Asymptotic distribution theory

Cramér-von Mises tests tests of goodness of fit tests of independence weak laws empirical processes Karhunen-Loève decompositions Gaussian processes Bessel functions


Deheuvels, Paul. Weighted multivariate Cramér-von Mises-type statistics. Afr. Stat. 1 (2005), no. 1, 1--14. doi:10.4314/afst.v1i1.46869.

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