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Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data

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  • Xu, Lin
  • Xiang, Sijia
  • Yao, Weixin

Abstract

A comprehensive longitudinal data analysis requires screening for unusual observations. Outliers or measurement errors might lead to considerable efficiency loss or even misleading results in longitudinal data inference. Via joint mean–covariance modelings (Pourahmadi, 2000; Zhang et al., 2015) and q-order entropy theory (Ferrari, 2010), we propose a maximum Lq-likelihood estimation for longitudinal data, which can yield robust and consistent estimators of the mean regression coefficients. An EM type algorithm is introduced to achieve both efficient and stable computation. The asymptotic properties of the proposed estimators are provided. Simulation studies and an application to Turkish anesthesiology data are used to show the effectiveness of the new approach.

Suggested Citation

  • Xu, Lin & Xiang, Sijia & Yao, Weixin, 2019. "Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 397-411.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:397-411
    DOI: 10.1016/j.jmva.2019.01.001
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    References listed on IDEAS

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    1. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    2. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
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    6. Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
    7. Yichen Qin & Carey E. Priebe, 2013. "Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 914-928, September.
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    Cited by:

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