TY - JOUR
T1 - New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis
AU - Fan, Jianqing
AU - Li, Runze
N1 - Funding Information:
Jianqing Fan is Professor of Statistics, Department of Operation Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). Runze Li is Assistant Professor, Department of Statistics, The Pennsylvania State University, University Park, PA 16802-2111 (E-mail: [email protected]). Fan’s research was supported in part by National Institute of Health grant R01 HL69720. Li’s research was supported by National Science Foundation grants DMS-01-02505 and DMS-03-48869 and a National Institute on Drug Abuse grant 1-P50-DA10075. The authors thank the associate editor and the referees for constructive comments that substantially improved an earlier draft, and the MACS study for the data used in Section 4.4.
PY - 2004/9
Y1 - 2004/9
N2 - Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models. The proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters. Rates of convergence of the resulting estimators are established. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures are shown to perform as well as an oracle estimator. A robust standard error formula is derived using a sandwich formula and is empirically tested. Local polynomial regression techniques are used to estimate the baseline function in the semiparametric model.
AB - Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models. The proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters. Rates of convergence of the resulting estimators are established. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures are shown to perform as well as an oracle estimator. A robust standard error formula is derived using a sandwich formula and is empirically tested. Local polynomial regression techniques are used to estimate the baseline function in the semiparametric model.
KW - Local polynomial regression
KW - Partial linear model
KW - Penalized least squares
KW - Profile least squares
KW - Smoothly clipped absolute deviation
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U2 - 10.1198/016214504000001060
DO - 10.1198/016214504000001060
M3 - Article
AN - SCOPUS:4944267519
SN - 0162-1459
VL - 99
SP - 710
EP - 723
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 467
ER -