Abstract:
We consider the asymptotic behavior of chi-square tests when a number kn of cells increases as the sample size n grows. For such a setting we show that a sequence of chi-square tests is asymptotically minimax if kn=o(n2) as n→∞. The proof makes use of a theorem about asymptotic normality of chi-square test statistics obtained under new assumptions.
Citation:
M. S. Ermakov, “Asymptotic minimaxity of chi-square tests”, Teor. Veroyatnost. i Primenen., 42:4 (1997), 668–695; Theory Probab. Appl., 42:4 (1998), 589–610
This publication is cited in the following 21 articles:
M. S. Ermakov, “O kriteriyakh tipa Neimana dlya proverki slozhnykh neparametricheskikh gipotez”, Veroyatnost i statistika. 36, Zap. nauchn. sem. POMI, 535, POMI, SPb., 2024, 120–140
M. S. Ermakov, “Chi-Squared Test for Hypothesis Testing of Homogeneity”, J Math Sci, 273:5 (2023), 763
Weige Tao, Guotao Wang, Zhigang Sun, Shuyan Xiao, Lingjiao Pan, Quanyu Wu, Min Zhang, “Feature optimization method for white feather broiler health monitoring technology”, Engineering Applications of Artificial Intelligence, 123 (2023), 106372
M. S. Ermakov, “On Uniform Consistency of Nonparametric Tests. II”, J Math Sci, 268:5 (2022), 629
M. S. Ermakov, “Kriterii khi-kvadrat dlya proverki gipotezy odnorodnosti”, Veroyatnost i statistika. 30, Zap. nauchn. sem. POMI, 501, POMI, SPb., 2021, 160–180
M. Ermakov, “On Uniform Consistency of Nonparametric Tests. I”, J Math Sci, 258:6 (2021), 802
M. S. Ermakov, “O ravnomernoi sostoyatelnosti neparametricheskikh kriteriev. II”, Veroyatnost i statistika. 29, Zap. nauchn. sem. POMI, 495, POMI, SPb., 2020, 147–176
M. S. Ermakov, “O ravnomernoi sostoyatelnosti neparametricheskikh kriteriev. I”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 98–147
Ji P., Nussbaum M., “Sharp Minimax Adaptation Over Sobolev Ellipsoids in Nonparametric Testing”, Electron. J. Stat., 11:2 (2017), 4515–4562
R. Bárcenas, J. Ortega, A. J. Quiroz, “Quadratic forms of the empirical processes for the two-sample problem for functional data”, TEST, 26:3 (2017), 503
Robins J.M., Li L., Tchetgen E.T., van der Vaart A., “Asymptotic normality of quadratic estimators”, Stoch. Process. Their Appl., 126:12, SI (2016), 3733–3759
Unnikrishnan J., Huang D., “Weak Convergence Analysis of Asymptotically Optimal Hypothesis Tests”, IEEE Trans. Inf. Theory, 62:7 (2016), 4285–4299
Kelly B.G., Wagner A.B., Tularak T., Viswanath P., “Classification of Homogeneous Data with Large Alphabets”, IEEE Trans. Inf. Theory, 59:2 (2013), 782–795
Huang D., Meyn S., “Generalized Error Exponents for Small Sample Universal Hypothesis Testing”, IEEE Trans. Inf. Theory, 59:12 (2013), 8157–8181
Huang D., Meyn S., “Error Exponents for Composite Hypothesis Testing with Small Samples”, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2012, 3261–3264
Huang D., Meyn S., “Classification with High-Dimensional Sparse Samples”, 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), IEEE International Symposium on Information Theory, IEEE, 2012
Dayu Huang, Sean Meyn, 2012 IEEE International Symposium on Information Theory Proceedings, 2012, 2586
Mikhail Ermakov, “Nonparametric signal detection with small type I and type II error probabilities”, Stat Inference Stoch Process, 14:1 (2011), 1
M. S. Ermakov, “On large deviations of type II error probabilities of Kolmogorov and omega-squared tests”, J. Math. Sci. (N. Y.), 128:1 (2005), 2538–2555
V. M. Kruglov, “The asymptotic behavior of the Pearson statistic”, Theory Probab. Appl., 45:1 (2001), 69–92
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