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Generalized partially linear models with missing covariates

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  • Liang, Hua

Abstract

In this article we study a semiparametric generalized partially linear model when the covariates are missing at random. We propose combining local linear regression with the local quasilikelihood technique and weighted estimating equation to estimate the parameters and nonparameters when the missing probability is known or unknown. We establish normality of the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. We apply the proposed models and methods to a study of the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. We also give simulation results to illustrate our approach.

Suggested Citation

  • Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:5:p:880-895
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    References listed on IDEAS

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    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
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    5. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    6. J. F. Lawless & J. D. Kalbfleisch & C. J. Wild, 1999. "Semiparametric methods for response‐selective and missing data problems in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 413-438, April.
    7. Lang Wu, 2004. "Exact and Approximate Inferences for Nonlinear Mixed-Effects Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 700-709, January.
    8. Joseph G. Ibrahim & Stuart R. Lipsitz & Nick Horton, 2001. "Using auxiliary data for parameter estimation with non‐ignorably missing outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 361-373.
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