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October 2016 Efficient estimation in semivarying coefficient models for longitudinal/clustered data
Ming-Yen Cheng, Toshio Honda, Jialiang Li
Ann. Statist. 44(5): 1988-2017 (October 2016). DOI: 10.1214/15-AOS1385

Abstract

In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are unknown and depend only on the index variable. First, we estimate the covariance matrices using residuals obtained from a preliminary estimation based on working independence and both spline and local linear regression. Then, using the covariance matrix estimates, we employ spline regression again to obtain our final estimator. It achieves the semiparametric efficiency bound under normality assumption and has the smallest asymptotic covariance matrix among a class of estimators even when normality is violated. Our theoretical results hold either when the number of within-subject observations diverges or when it is uniformly bounded. In addition, using the local linear estimator of the nonparametric component is superior to using the spline estimator in terms of numerical performance. The proposed method is compared with the working independence estimator and some existing method via simulations and application to a real data example.

Citation

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Ming-Yen Cheng. Toshio Honda. Jialiang Li. "Efficient estimation in semivarying coefficient models for longitudinal/clustered data." Ann. Statist. 44 (5) 1988 - 2017, October 2016. https://doi.org/10.1214/15-AOS1385

Information

Received: 1 June 2015; Revised: 1 September 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1349.62128
MathSciNet: MR3546441
Digital Object Identifier: 10.1214/15-AOS1385

Subjects:
Primary: 62G08

Keywords: covariance matrix estimation , local linear regression , semiparametric efficiency bound , Spline functions

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • October 2016
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