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Biometrika 2002 89(3):579-590; doi:10.1093/biomet/89.3.579
© 2002 by Biometrika Trust
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Estimation in a semiparametric model for longitudinal data with unspecified dependence structure

Xuming He1, Zhong-Yi Zhu2 and Wing-Kam Fung3

1 Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, Illinois 61820, U.S.Ax-he{at}uiuc.edu 2 Department of Statistics, China East Normal University, Shanghai, China zyzhu{at}stat.ecnu.edu.cn 3 Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China wingfung{at}hku.hk

This paper considers an extension of M-estimators in semiparametric models for independent observations to the case of longitudinal data.We approximate the nonparametric function by a regression spline, and any M-estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid large-sample inferences about the regression parameters without any specification of the error distribution and the covariance structure. Included as special cases are the analysis of the conditional mean and median functions for longitudinal data.

Key Words: B-spline; M-estimator; Mixed model; Rate of convergence; Regression median; Repeated measures

Received November 2000. Revised November 2001


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