Geodesic
Chi-squared test for testing of homogeneity
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 160-180 Cet article a éte moissonné depuis la source Math-Net.Ru

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We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size growth. Nonparametric sets of alternatives can be defined both in terms of densities and distribution functions. 
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M. S. Ermakov. Chi-squared test for testing of homogeneity. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 160-180. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a10/

[1] N. Anderson, P. Hall, D. Titterington, “Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates”, J. Multivariate Anal., 50 (1994), 41–54 | DOI | MR | Zbl

[2] B. M. Brown, “Martingale central limit theorems”, Ann. Math. Statist., 42 (1971), 59–66 | DOI | MR | Zbl

[3] A. R. Barron, “Uniformly powerful goodness of fit tests”, Ann. Statist., 17 (1989), 107–124 | DOI | MR | Zbl

[4] D. M. Chibisov, “Asymptotic optimality of the chi-square test with large number of degrees of freedom within the class of symmetric tests”, Math. Methods Statist., 1 (1992), 55–82 | MR | Zbl

[5] M. S. Ermakov, “Asimptoticheskaya minimaksnost kriteriev khi-kvadrat”, Teoriya veroyatn. i ee primen., 42 (1997), 668–695 | Zbl

[6] M. S. Ermakov, “O ravnomernoi sostoyatelnosti neparametricheskikh kriteriev. I”, Zap. nuchn. semin. POMI, 495, 2020, 147–176

[7] M. Fromont, B. Laurent, M. Lerasle, P. Reynaud-Bouret, “Kernels based tests with non-asymptotic bootstrap approaches for two-sample problem”, JMLR: Workshop and Conference Proceedings, 23 (2012), 23–41

[8] M. Fromont, B. Laurent, P. Reynaud-Bouret, “The two-sample problem for poisson processes: Adaptive tests with a nonasymptotic wild bootstrap approach”, The Annals of Statistics, 41 (2013), 1431–1461 | DOI | MR | Zbl

[9] A. Gretton, K. Borgwardt, M. Rasch, B. Scholkopf, A. Smola, “A kernel two-sample test”, J. Machine Learning Research, 13 (2012), 723–773 | MR | Zbl

[10] A. Gretton, D. Sejdinovic, H. Strathmann, S. Balakrishnan, M. Pontil, K. Fukumizu, B. K. Sriperumbudur, “Optimal kernel choice for large-scale two-sample tests”, Advances Neural Information Processing systems, 2012, 1205–1213

[11] P. Hall, “Central limit theorem for integrated square error of multivariate nonparametric density estimators”, J. Multivariate Analysis, 14 (1984), 1–16 | DOI | MR | Zbl

[12] G. I. Ivchenko, Ya. Yu. Medvedev, “Razdelimye statistiki i proverka gipotez dlya gruppirovannykh dannykh”, Teoriya veroyatn. i ee primen., 25 (1980), 549–560 | Zbl

[13] Yu. I. Ingster, “O sravnenii minimaksnykh svoistv testov Kolmogorova, $\omega^2$ i $\chi^2$”, Teor. veroyatn. i ee primen., 32 (1987), 374–378 | MR | Zbl

[14] Yu. I. Ingster, I. A. Suslina, Nonparametric Goodness-of-fit Testing under Gaussian Models, Lecture Notes in Statistics, 169, Springer, N.Y., 2002

[15] H. B. Mann, A. Wald, “On the choice of the number of intervals in the application of chi-squared test”, Ann. Math. Statist., 13 (1942), 306–318 | DOI

[16] C. Morris, “Central limit theorems for multinomial sums”, Ann. Statist., 3 (1975), 165–188 | DOI | MR | Zbl

[17] J. Robins, L. Li, E. T. Tchetgen, Aad van der Vaart, “Asymptotic Normality of Quadratic Estimators”, Stochastic Processes and their Applications, 126 (2015), 3733–3759 | DOI

[18] T. Li, M. Yuan, On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives, 2019, 42 pp., arXiv: 1909.03302