Semiparametric estimation of covariance matrixes for longitudinal data

Jianqing Fan, Yichao Wu

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


Estimation of longitudinal data covariance structure poses significant challenges because the data usually are collected at irregular time points. A viable semiparametric model for covariance matrixes has been proposed that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically by aggregating information from irregular and sparse data points within each subject. But the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. We address this problem in the context of more general models for the conditional mean function, including parametric, nonparametric, or semiparametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression models. This provides a more robust estimator of the covariance function under a wider range of situations. Under some technical conditions, consistency and asymptotic normality are obtained for the QMLE of the parameters in the correlation function. Simulation studies and a real data example are used to illustrate the proposed approach.

Original languageEnglish (US)
Pages (from-to)1520-1533
Number of pages14
JournalJournal of the American Statistical Association
Issue number484
StatePublished - Dec 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Correlation structure
  • Difference-based estimation
  • Quasi-maximum likelihood
  • Varying-coefficient partially linear model


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