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On the asymptotic distribution of T2-type statistic with two-step monotone missing data

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Abstract

In this article, we consider the asymptotic distribution of Hotelling’s T2-type test statistic when a two-step monotone missing data set is drawn from a multivariate normal population under a large-sample asymptotic framework. In particular, asymptotic expansions for the distribution and upper percentiles are derived using a perturbation method up to the terms of order n−1, where n = N-2 and N denotes the total sample size. Furthermore, making use of Fujikoshi’s transformations, we also have Bartlett-type corrections of the test statistic considered in this article. Finally, we investigate the performance of the proposed approximation to the upper percentiles and Bartletttype correction for the test statistic by conducting Monte Carlo simulations for some selected parameters.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, Tokyo University of Science, Tokyo, Japan

    Tamae Kawasaki & Takashi Seo

  2. Graduate School of Maritime Sciences, Kobe University, 5-1-1, Fukae-minamimachi, Higashinada-ku Kobe-shi, Hyogo, 658-0022, Japan

    Nobumichi Shutoh

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  1. Tamae Kawasaki
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  2. Nobumichi Shutoh
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  3. Takashi Seo
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Correspondence to Nobumichi Shutoh.

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Kawasaki, T., Shutoh, N. & Seo, T. On the asymptotic distribution of T2-type statistic with two-step monotone missing data. J Stat Theory Pract 12, 657–668 (2018). https://doi.org/10.1080/15598608.2018.1450795

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  • DOI: https://doi.org/10.1080/15598608.2018.1450795

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