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On Neyman-type smooth tests of fit. (English) Zbl 0733.62051

Summary: Some quadratic tests of fit related to Neyman’s smooth tests as well as to a class of quadratic tests of fit introduced recently by G. Neuhaus [Ann. Stat. 16, No.3, 1342-1343 (1988; Zbl 0664.62015)] are considered. Attention is focused on the case of completely specified null distributions. The case when the number of summands in the test statistics goes to infinity is discussed. In this case, the asymptotic distribution under the null hypothesis as well as under some sequences of alternatives are derived by means of the Komlós, Major and Tusnády embedding. Using the same technique, the asymptotic distribution of the classical chi-square test is investigated in the case when the number of cells tends to infinity.

MSC:

62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0664.62015
Full Text: DOI

References:

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