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Data driven chi-square test for uniformity with unequal cells. (English) Zbl 1054.62057

Summary: The power of Pearson’s chi-square test for uniformity depends heavily on the choice of the partition of the unit interval involved in the form of the test statistic. We propose a selection rule which chooses a proper partition based on the data. This selection rule leads usually to essentially unequal cells well suited to the observed distribution. We investigate the corresponding data driven chi-square test and present a Monte Carlo simulation study. The conclusion is that this test achieves a high and very stable power for a large class of alternatives, and is much more stable than any other test we compare to.

MSC:

62G10 Nonparametric hypothesis testing
65C05 Monte Carlo methods
62G20 Asymptotic properties of nonparametric inference
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