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A multivariate Kolmogorov-Smirnov test of goodness of fit. (English) Zbl 0883.62054
Summary: This paper presents a distribution-free multivariate Kolmogorov-Smirnov goodness-of-fit test. The test uses a statistic which is built using M. Rosenblatt’s [Ann. Math. Stat. 23, 470-472 (1952; Zbl 0047.13104)] transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulation study.

MSC:
62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
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