Analysis of longitudinal data with semiparametric estimation of covariance function

Jianqing Fan, Tao Huang, Runze Li

Research output: Contribution to journalArticle

151 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)632-641
Number of pages10
JournalJournal of the American Statistical Association
Volume102
Issue number478
DOIs
StatePublished - Jun 1 2007

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Semiparametric Estimation
Covariance Function
Longitudinal Data
Variance Function
Correlation Structure
Generalized Variance
Partially Linear Model
Varying Coefficients
Quasi-likelihood
Minimum Variance
Kernel Estimator
Weighted Least Squares
Semiparametric Model
Regression Coefficient
Asymptotic Normality
Irregular
Monte Carlo Simulation
Simulation Study
Trajectory
Estimator

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "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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Analysis of longitudinal data with semiparametric estimation of covariance function. / Fan, Jianqing; Huang, Tao; Li, Runze.

In: Journal of the American Statistical Association, Vol. 102, No. 478, 01.06.2007, p. 632-641.

Research output: Contribution to journalArticle

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