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

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.

Keywords:

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

Acknowledgments

The authors express sincere thanks to the Editor, the Associate Editor and two anonymous referees for their constructive and valuable suggestions on this article, which have led to significant improvements.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.