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

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

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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.

Original languageEnglish (US)
Pages (from-to)531-549
Number of pages19
JournalJournal of Nonparametric Statistics
Volume28
Issue number3
DOIs
Publication statusPublished - Jul 2 2016

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Keywords

  • asymptotic bias and risk
  • likelihood ratio test
  • longitudinal data
  • partially linear model
  • pretest and shrinkageestimators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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