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

• Published in: Journal of nonparametric statistics Vol. 28; no. 3; pp. 531 - 549
• Main Authors: Hossain, S., Ahmed, S. Ejaz, Yi, Grace Y., Chen, B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.07.2016; Taylor & Francis Ltd
• Subjects: asymptotic bias and risk; Asymptotic properties; Constrictions; Data analysis; Economic models; Estimating techniques; Estimators; Least squares method; likelihood ratio test; longitudinal data; Mathematical analysis; Mathematical models; partially linear model; Performance evaluation; pretest and shrinkageestimators; Risk; Shrinkage
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2016.1190358

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.