TY - JOUR
T1 - Analysis of longitudinal data with semiparametric estimation of covariance function
AU - Fan, Jianqing
AU - Huang, Tao
AU - Li, Runze
N1 - Funding Information:
Jianqing Fan is Frederick Moore Professor of Finance, Department of Operation Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). Tao Huang is Assistant Professor, Department of Statistics, University of Virginia, Charlottesville, VA 22904 (E-mail: [email protected]). Runze Li is Associate Professor, Department of Statistics and the Methodology Center, Pennsylvania State University, University Park, PA 16802 (E-mail: [email protected]). Fan’s research was supported in part by National Science Foundation (NSF) grant DMS-03-54223 and National Institutes of Health grant R01-GM072611. Li’s research was supported by NSF grant DMS-03-48869 and National Institute on Drug Abuse grant P50 DA10075. The authors thank the associate editor and the referees for their constructive comments that substantially improved an earlier draft, and the MACS study for the data used in Section 5.3.
PY - 2007/6
Y1 - 2007/6
N2 - Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure - a quasi-likelihood approach and a minimum generalized variance method - are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies. The proposed methodology is illustrated with an analysis of a real data example.
AB - Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure - a quasi-likelihood approach and a minimum generalized variance method - are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies. The proposed methodology is illustrated with an analysis of a real data example.
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U2 - 10.1198/016214507000000095
DO - 10.1198/016214507000000095
M3 - Article
C2 - 19707537
AN - SCOPUS:34250768880
SN - 0162-1459
VL - 102
SP - 632
EP - 641
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 478
ER -