New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis

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.

[1]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[2]  J. Phair,et al.  The Multicenter AIDS Cohort Study: rationale, organization, and selected characteristics of the participants. , 1987, American journal of epidemiology.

[3]  P. Speckman.  Kernel smoothing in partial linear models , 1988 .

[4]  Jianqing Fan.  Design-adaptive Nonparametric Regression , 1992 .

[5]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[6]  H. Müller,et al.  On variance function estimation with quadratic forms , 1993 .

[7]  Peter J. Diggle,et al.  RATES OF CONVERGENCE IN SEMI‐PARAMETRIC MODELLING OF LONGITUDINAL DATA , 1994 .

[8]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[9]  P. Diggle,et al.  Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. , 1994, Biometrics.

[10]  T. Severini,et al.  Quasi-Likelihood Estimation in Semiparametric Models , 1994 .

[11]  M. Wand,et al.  An Effective Bandwidth Selector for Local Least Squares Regression , 1995 .

[12]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[13]  L. Breiman.  Heuristics of instability and stabilization in model selection , 1996 .

[14]  Jianqing Fan,et al.  Generalized Partially Linear Single-Index Models , 1997 .

[15]  P. Diggle,et al.  Analysis of Longitudinal Data. , 1997 .

[16]  Chin-Tsang Chiang,et al.  Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data , 1998 .

[17]  Li Ping Yang,et al.  Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data , 1998 .

[18]  Torben Martinussen,et al.  A semiparametric additive regression model for longitudinal data , 1999 .

[19]  Jianqing Fan,et al.  Two‐step estimation of functional linear models with applications to longitudinal data , 1999 .

[20]  Lee-Jen Wei,et al.  Inferences for a semiparametric model with panel data , 2000 .

[21]  R. Carroll,et al.  Semiparametric Regression for Clustered Data Using Generalized Estimating Equations , 2001 .

[22]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[23]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[24]  Jianqing Fan,et al.  Generalized likelihood ratio statistics and Wilks phenomenon , 2001 .

[25]  Jianqing Fan,et al.  Regularization of Wavelet Approximations , 2001 .

[26]  Torben Martinussen,et al.  Sampling Adjusted Analysis of Dynamic Additive Regression Models for Longitudinal Data , 2001 .

[27]  Chin-Tsang Chiang,et al.  Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables , 2001 .

[28]  Zhiliang Ying,et al.  Semiparametric and Nonparametric Regression Analysis of Longitudinal Data , 2001 .

[29]  Jianhua Z. Huang,et al.  Varying‐coefficient models and basis function approximations for the analysis of repeated measurements , 2002 .

[30]  조재현.  Goodness of fit tests for parametric regression models , 2004 .

[31]  R. Carroll,et al.  Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data , 2005 .