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Two-sample test for sparse high-dimensional multinomial distributions

Author

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  • Amanda Plunkett

    (Department of Defense)

  • Junyong Park

    (University of Maryland Baltimore County)

Abstract

In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical Chi-square test may have some drawbacks in this case since many of cell counts may be zero or may not be large enough. We propose a new test and show its asymptotic normality and the asymptotic power function. Based on the asymptotic power function, we present an application of our result to a neighborhood-type test which has been previously studied, especially for the case of fairly small p values. To compare the proposed test with existing tests, we provide numerical studies including simulations and real data examples.

Suggested Citation

  • Amanda Plunkett & Junyong Park, 2019. "Two-sample test for sparse high-dimensional multinomial distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 804-826, September.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0600-8
    DOI: 10.1007/s11749-018-0600-8
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    References listed on IDEAS

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    4. Munk, A. & Paige, R. & Pang, J. & Patrangenaru, V. & Ruymgaart, F., 2008. "The one- and multi-sample problem for functional data with application to projective shape analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 815-833, May.
    5. Junyong Park & Bimal Sinha & Arvind Shah & Dihua Xu & Jianxin Lin, 2015. "Likelihood Ratio Tests for Interval Hypotheses with Applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2351-2370, June.
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