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Shrinkage and pretest estimators for longitudinal data analysis under partially linear models

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  • S. Hossain
  • S. Ejaz Ahmed
  • Grace Y. Yi
  • B. Chen

Abstract

In this paper, we develop marginal analysis methods for longitudinal data under partially linear models. We employ the pretest and shrinkage estimation procedures to estimate the mean response parameters as well as the association parameters, which may be subject to certain restrictions. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators, and investigate their relative performance to the unrestricted semiparametric least-squares estimator (USLSE). We show that if the dimension of association parameters exceeds two, the risk of the shrinkage estimators is strictly less than that of the USLSE in most of the parameter space. On the other hand, the risk of the pretest estimator depends on the validity of the restrictions of association parameters. A simulation study is conducted to evaluate the performance of the proposed estimators relative to that of the USLSE. A real data example is applied to illustrate the practical usefulness of the proposed estimation procedures.

Suggested Citation

  • S. Hossain & S. Ejaz Ahmed & Grace Y. Yi & B. Chen, 2016. "Shrinkage and pretest estimators for longitudinal data analysis under partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 531-549, September.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:531-549
    DOI: 10.1080/10485252.2016.1190358
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    References listed on IDEAS

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    Cited by:

    1. Shakhawat Hossain & Le An Lac, 2021. "Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 811-835, December.
    2. Shakhawat Hossain & Trevor Thomson & Ejaz Ahmed, 2018. "Shrinkage estimation in linear mixed models for longitudinal data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 569-586, July.

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