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Robust inference for generalized partially linear mixed models that account for censored responses and missing covariates -- an application to Arctic data analysis

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  • Kalyan Das
  • Angshuman Sarkar

Abstract

In this article, we propose a family of bounded influence robust estimates for the parametric and non-parametric components of a generalized partially linear mixed model that are subject to censored responses and missing covariates. The asymptotic properties of the proposed estimates have been looked into. The estimates are obtained by using Monte Carlo expectation--maximization algorithm. An approximate method which reduces the computational time to a great extent is also proposed. A simulation study shows that performances of the two approaches are similar in terms of bias and mean square error. The analysis is illustrated through a study on the effect of environmental factors on the phytoplankton cell count.

Suggested Citation

  • Kalyan Das & Angshuman Sarkar, 2014. "Robust inference for generalized partially linear mixed models that account for censored responses and missing covariates -- an application to Arctic data analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2418-2436, November.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:11:p:2418-2436
    DOI: 10.1080/02664763.2014.910886
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    1. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    2. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    3. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    4. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    5. James P. Hughes, 1999. "Mixed Effects Models with Censored Data with Application to HIV RNA Levels," Biometrics, The International Biometric Society, vol. 55(2), pages 625-629, June.
    6. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
    7. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    8. Vonesh E. F. & Wang H. & Nie L. & Majumdar D., 2002. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 271-283, March.
    9. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
    10. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
    11. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    12. Hulin Wu & A. Adam Ding, 1999. "Population HIV-1 Dynamics In Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials," Biometrics, The International Biometric Society, vol. 55(2), pages 410-418, June.
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    Cited by:

    1. Das, Ujjwal & Das, Kalyan, 2018. "Inference on zero inflated ordinal models with semiparametric link," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 104-115.

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