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Bartlett's Decomposition of the Posterior Distribution of the Covariance for Normal Monotone Ignorable Missing Data

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  • Liu, C. H.

Abstract

This paper presents a decomposition for the posterior distribution of the covarianee matrix of normal models under a family of prior distributions when missing data are ignorable and monotone. This decomposition is an extension of Bartlett's decomposition of the Wishart distribution to monotone missing data. It is not only theoretically interesting but also practically useful. First, with monotone missing data, it allows more efficient drawing of parameters from the posterior distribution than the factorized likelihood approach. Furthermore, with nonmonotone missing data, it allows for a very efficient monotone date augmentation algorithm and thereby multiple imputation or the missing data needed to create a monotone pattern.

Suggested Citation

  • Liu, C. H., 1993. "Bartlett's Decomposition of the Posterior Distribution of the Covariance for Normal Monotone Ignorable Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 198-206, August.
    • Handle: RePEc:eee:jmvana:v:46:y:1993:i:2:p:198-206
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    Cited by:

    1. Liu, Chuanhai, 1999. "Efficient ML Estimation of the Multivariate Normal Distribution from Incomplete Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 206-217, May.
    2. Tang, Yongqiang, 2015. "An efficient monotone data augmentation algorithm for Bayesian analysis of incomplete longitudinal data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 146-152.
    3. Gillen, Benjamin J., 2014. "An empirical Bayesian approach to stein-optimal covariance matrix estimation," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 402-420.

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