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Finite-sample inference with monotone incomplete multivariate normal data, I

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  • Chang, Wan-Ying
  • Richards, Donald St.P.

Abstract

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from , a multivariate normal population with mean and covariance matrix . We derive a stochastic representation for the exact distribution of , the maximum likelihood estimator of . We obtain ellipsoidal confidence regions for through T2, a generalization of Hotelling's statistic. We derive the asymptotic distribution of, and probability inequalities for, T2 under various assumptions on the sizes of the complete and incomplete samples. Further, we establish an upper bound for the supremum distance between the probability density functions of and , a normal approximation to .

Suggested Citation

  • Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:1883-1899
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    References listed on IDEAS

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    1. R. Bhargava, 1975. "Some one-sample hypothesis testing problems when there is a monotone sample from a multivariate normal population," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 327-339, December.
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    5. Andersson, S. A. & Perlman, M. D., 1995. "Testing Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 18-38, April.
    6. Andersson, S. A. & Perlman, M. D., 1995. "Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 1-17, April.
    7. K. Krishnamoorthy & Maruthy Pannala, 1998. "Some Simple Test Procedures for Normal Mean Vector with Incomplete Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 531-542, September.
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    Citations

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    Cited by:

    1. Tomoya Yamada & Megan Romer & Donald Richards, 2015. "Kurtosis tests for multivariate normality with monotone incomplete data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 532-557, September.
    2. Krishnamoorthy, K., 2013. "Comparison of confidence intervals for correlation coefficients based on incomplete monotone samples and those based on listwise deletion," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 378-388.
    3. Tsukada, Shin-ichi, 2014. "Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 183-196.
    4. Richards, Donald St. P. & Yamada, Tomoya, 2010. "The Stein phenomenon for monotone incomplete multivariate normal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 657-678, March.
    5. Romer, Megan M. & Richards, Donald St. P., 2010. "Maximum likelihood estimation of the mean of a multivariate normal population with monotone incomplete data," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1284-1288, September.
    6. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.
    7. Keiji Takai & Kenichi Hayashi, 2023. "Model Selection with Missing Data Embedded in Missing-at-Random Data," Stats, MDPI, vol. 6(2), pages 1-11, April.
    8. Chang, Wan-Ying & Richards, Donald St. P., 2010. "Finite-sample inference with monotone incomplete multivariate normal data, II," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 603-620, March.

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