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Missing Data Imputation Using the Multivariate t Distribution

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  • Liu, C.

Abstract

When a rectangular multivariate data set contains missing values, missing data imputation using the multivariate t distribution appears potentially useful, especially for robust inferences. An efficient technique, called the monotone data augmentation algorithm, for implementing missing data imputation using the multivariate t distribution with known and unknown weights, with monotone and nonmonotone missing data, and with known and unknown degrees of freedom is presented. Two numerical examples are included to illustrate the methodology, to compare results obtained using the multivariate t distribution with results obtained using the normal distribution, and to compare the rate of convergence of the monotone data augmentation algorithm with the rate of convergence of the (rectangular) data augmentation algorithm.

Suggested Citation

  • Liu, C., 1995. "Missing Data Imputation Using the Multivariate t Distribution," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 139-158, April.
  • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:139-158
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    References listed on IDEAS

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    1. Dielman, Terry E. & Rose, Elizabeth L., 1996. "A note on hypothesis testing in LAV multiple regression: A small sample comparison," Computational Statistics & Data Analysis, Elsevier, pages 463-470.
    2. Dielman, Terry E. & Rose, Elizabeth L., 1995. "A bootstrap approach to hypothesis testing in least absolute value regression," Computational Statistics & Data Analysis, Elsevier, pages 119-130.
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    Cited by:

    1. Tang, Yongqiang, 2015. "An efficient monotone data augmentation algorithm for Bayesian analysis of incomplete longitudinal data," Statistics & Probability Letters, Elsevier, pages 146-152.
    2. Jie Jiang & Xinsheng Liu & Keming Yu, 2013. "Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution," Computational Statistics, Springer, vol. 28(4), pages 1485-1500, August.
    3. Sik-Yum Lee & Ye-Mao Xia, 2008. "A Robust Bayesian Approach for Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, pages 343-364.
    4. Margaret Y Hwang & David Weil, 1997. "The Diffusion of Modern Manufacturing Practices: Evidence from Retail-Apparel Sectors," Working Papers 97-11, Center for Economic Studies, U.S. Census Bureau.
    5. Atkinson, A. C. & Cheng, Tsung-Chi, 2000. "On robust linear regression with incomplete data," Computational Statistics & Data Analysis, Elsevier, pages 361-380.

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