Goodness-of-fit and comparison tests of the Kolmogorov-Smirnov type for bivariate populations. (English) Zbl 0817.62035

Cabaña, Alejandra; Cabaña, Enrique M.

Ann. Stat. 22, No. 3, 1447-1459 (1994).

Summary: 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 their computation and empirical estimations of the power of the tests are given.

MSC:

62G10	Nonparametric hypothesis testing
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60J65	Brownian motion

Keywords:

empirical measure transformations; bivariate Kolmogorov-Smirnov tests; tail estimates for functionals of Wiener sheets; goodness-of-fit; two- sample comparisons; normalized empirical processes; Brownian bridge