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Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data

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  • Daniel Gaigall

    (Leibniz Universität Hannover)

Abstract

We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.

Suggested Citation

  • Daniel Gaigall, 2020. "Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 437-465, May.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00742-5
    DOI: 10.1007/s00184-019-00742-5
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    References listed on IDEAS

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    1. Hani M. Samawi & Robert Vogel, 2014. "Notes on two sample tests for partially correlated (paired) data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 109-117, January.
    2. Reza Modarres, 2008. "Tests of Bivariate Exchangeability," International Statistical Review, International Statistical Institute, vol. 76(2), pages 203-213, August.
    3. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.
    4. Akritas, Michael G. & Antoniou, Efi S. & Kuha, Jouni, 2006. "Nonparametric Analysis of Factorial Designs With Random Missingness: Bivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1513-1526, December.
    5. Yu, Donghyeon & Lim, Johan & Liang, Feng & Kim, Kyunga & Kim, Byung Soo & Jang, Woncheol, 2012. "Permutation test for incomplete paired data with application to cDNA microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 510-521.
    6. Konietschke, F. & Harrar, S.W. & Lange, K. & Brunner, E., 2012. "Ranking procedures for matched pairs with missing data — Asymptotic theory and a small sample approximation," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1090-1102.
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