New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis

Jianqing Fan, Runze Li

Research output: Contribution to journalArticlepeer-review

299 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)710-723
Number of pages14
JournalJournal of the American Statistical Association
Volume99
Issue number467
DOIs
StatePublished - Sep 2004

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Local polynomial regression
  • Partial linear model
  • Penalized least squares
  • Profile least squares
  • Smoothly clipped absolute deviation

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