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Teor. Veroyatnost. i Primenen., 1997, Volume 42, Issue 4, Pages 668–695 (Mi tvp2179)  

This article is cited in 9 scientific papers (total in 9 papers)

Asymptotic minimaxity of chi-square tests

M. S. Ermakov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We consider the asymptotic behavior of chi-square tests when a number $k_n$ 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 $k_n = o(n^2)$ as $n \to \infty$. The proof makes use of a theorem about asymptotic normality of chi-square test statistics obtained under new assumptions.

Keywords: chi-square tests, asymptotic efficiency, asymptotic normality, asymptotically minimax approach, goodness-of-fit testing.

DOI: https://doi.org/10.4213/tvp2179

Full text: PDF file (1297 kB)

English version:
Theory of Probability and its Applications, 1998, 42:4, 589–610

Bibliographic databases:

Received: 11.11.1996

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

Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 4
\pages 589--610
\crossref{https://doi.org/10.1137/S0040585X97976441}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Kruglov, “Complete convergence of the Pearson statistic”, Math. Notes, 66:4 (1999), 515–519  mathnet  crossref  crossref  mathscinet  isi
    2. 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  mathnet  crossref  mathscinet  zmath
    3. 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  crossref  isi  scopus
    4. 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  isi
    5. 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  crossref  mathscinet  zmath  isi  elib  scopus
    6. Huang D., Meyn S., “Generalized Error Exponents for Small Sample Universal Hypothesis Testing”, IEEE Trans. Inf. Theory, 59:12 (2013), 8157–8181  crossref  mathscinet  zmath  isi  scopus
    7. 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  crossref  mathscinet  zmath  isi  scopus
    8. Unnikrishnan J., Huang D., “Weak Convergence Analysis of Asymptotically Optimal Hypothesis Tests”, IEEE Trans. Inf. Theory, 62:7 (2016), 4285–4299  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ji P., Nussbaum M., “Sharp Minimax Adaptation Over Sobolev Ellipsoids in Nonparametric Testing”, Electron. J. Stat., 11:2 (2017), 4515–4562  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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