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Transformed Empirical Processes and Modified Kolmogorov-Smirnov Tests for Multivariate Distributions

A. Cabana and E. M. Cabana
The Annals of Statistics
Vol. 25, No. 6 (Dec., 1997), pp. 2388-2409
Stable URL: http://www.jstor.org/stable/2959038
Page Count: 22
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Transformed Empirical Processes and Modified Kolmogorov-Smirnov Tests for Multivariate Distributions
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Abstract

A general way of constructing classes of goodness-of-fit tests for multivariate samples is presented. These tests are based on a random signed measure that plays the same role as the empirical process in the construction of the classical Kolmogorov-Smirnov tests. The resulting tests are consistent against any fixed alternative, and, for each sequence of contiguous alternatives, a test in each class can be chosen so as to optimize the discrimination of those alternatives.

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