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Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data

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  • Ke-Hai Yuan
  • Wai Chan
  • Yubin Tian

Abstract

Means and covariance/dispersion matrix are the building blocks for many statistical analyses. By naturally extending the score functions based on a multivariate $$t$$ t -distribution to estimating equations, this article defines a class of M-estimators of means and dispersion matrix for samples with missing data. An expectation-robust (ER) algorithm solving the estimating equations is obtained. The obtained relationship between the ER algorithm and the corresponding estimating equations allows us to obtain consistent standard errors when robust means and dispersion matrix are further analyzed. Estimating equations corresponding to existing ER algorithms for computing M- and S-estimators are also identified. Monte Carlo results show that robust methods outperform the normal-distribution-based maximum likelihood when the population distribution has heavy tails or when data are contaminated. Applications of the results to robust analysis of linear regression and growth curve models are discussed. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Suggested Citation

  • Ke-Hai Yuan & Wai Chan & Yubin Tian, 2016. "Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 329-351, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:329-351
    DOI: 10.1007/s10463-014-0498-1
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    References listed on IDEAS

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    1. Ke-Hai Yuan & Fan Yang-Wallentin & Peter M. Bentler, 2012. "ML Versus MI for Missing Data With Violation of Distribution Conditions," Sociological Methods & Research, , vol. 41(4), pages 598-629, November.
    2. Ke-Hai Yuan & Peter Bentler & Wai Chan, 2004. "Structural equation modeling with heavy tailed distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 421-436, September.
    3. Roderick J. A. Little, 1988. "Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 23-38, March.
    4. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    5. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    6. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
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    Cited by:

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    2. Ke-Hai Yuan & Mortaza Jamshidian & Yutaka Kano, 2018. "Missing Data Mechanisms and Homogeneity of Means and Variances–Covariances," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 425-442, June.

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