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On Uniform Consistency of Nonparametric Tests. I

For widespread nonparametric tests, we point out necessary and sufficient conditions of uniform consistency for nonparametric sets of alternatives. Nonparametric sets of alternatives can be defined both in terms of distribution functions and in terms of density. Such conditions are provided for χ2-tests with an increasing number of cells, for Cramér – von Mises tests, for tests generated by 𝕃2-norms of kernel estimators, and for tests generated by quadratic forms of estimators of Fourier coefficients. Necessary and sufficient conditions on sets of alternatives for the existence of uniformly consistent tests are treated as well.

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Correspondence to M. Ermakov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 98–147.

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Ermakov, M. On Uniform Consistency of Nonparametric Tests. I. J Math Sci 258, 802–837 (2021).

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