The Annals of Statistics

Goodness-of-Fit and Comparison Tests of the Kolmogorov-Smirnov Type for Bivariate Populations

Alejandra Cabana and Enrique M. Cabana

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Abstract

Statistical tests consistent under any alternative are provided for both goodness-of-fit and two-sample comparisons. They are based on (1) the derivation of estimates for the tails of the probability distribution of some particular functionals of a Wiener sheet and (2) the use of a mapping that carries normalized empirical processes (asymptotically distributed as Brownian bridge) onto new processes that converge in distribution to a Wiener sheet. The proposed test statistics are easily obtained from the data. Hints for its computation and empirical estimations of the power of the tests are given.

Article information

Source
Ann. Statist., Volume 22, Number 3 (1994), 1447-1459.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325636

Digital Object Identifier
doi:10.1214/aos/1176325636

Mathematical Reviews number (MathSciNet)
MR1311983

Zentralblatt MATH identifier
0817.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 60G60: Random fields 60G15: Gaussian processes

Keywords
Wiener sheet empirical measure transformations bivariate Kolmogorov-Smirnov tests tail estimates for functionals of Wiener sheet

Citation

Cabana, Alejandra; Cabana, Enrique M. Goodness-of-Fit and Comparison Tests of the Kolmogorov-Smirnov Type for Bivariate Populations. Ann. Statist. 22 (1994), no. 3, 1447--1459. doi:10.1214/aos/1176325636. https://projecteuclid.org/euclid.aos/1176325636


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