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Maximum likelihood estimation of the mean of a multivariate normal population with monotone incomplete data

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  • Romer, Megan M.
  • Richards, Donald St. P.

Abstract

Given a two-step, monotone incomplete, random sample from , a multivariate normal population with mean and covariance matrix , we consider the problem of deriving an exact stochastic representation for , the maximum likelihood estimator of . We prove that and , the maximum likelihood estimators of and , respectively, are equivariant under a certain group of affine transformations, and then we apply the equivariance property to obtain a new derivation of a stochastic representation for established by Chang and Richards (2009). The new derivation induces explicit representations, in terms of the data, for the independent random variables that arise in the stochastic representation for .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1284-1288
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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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    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.

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