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Two-stage efficient estimation of longitudinal nonparametric additive models

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  • You, Jinhong
  • Zhou, Haibo

Abstract

Nonparametric smoothings are useful tool to model longitudinal data. In this paper we study the estimating problem of longitudinal nonparametric additive regression models. A two-stage efficient approach is developed to estimate the unknown additive components. We show the resulted estimators have some advantages over the existed ones. For example, they are asymptotically more efficient than those neglecting the dependence of repeated observations over time within the same subject, have an oracle property, that is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty, and can be naturally extended to deal with generalized longitudinal nonparametric additive regression model. The asymptotic normality is established for the underlying additive components. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.

Suggested Citation

  • You, Jinhong & Zhou, Haibo, 2007. "Two-stage efficient estimation of longitudinal nonparametric additive models," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1666-1675, November.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:17:p:1666-1675
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    References listed on IDEAS

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    2. 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.
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    6. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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    Cited by:

    1. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).

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