Two-step estimation of functional linear models with applications to longitudinal data

Jianqing Fan, Jin Ting Zhang

Research output: Contribution to journalArticlepeer-review

343 Scopus citations


Functional linear models are useful in longitudinal data analysis. They include many classical and recently proposed statistical models for longitudinal data and other functional data. Recently, smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance. To overcome these drawbacks, in this paper, a simple and powerful two-step alternative is proposed. In particular, the implementation of the proposed approach via local polynomial smoothing is discussed. Methods for estimating standard deviations of estimated coefficient functions are also proposed. Some asymptotic results for the local polynomial estimators are established. Two longitudinal data sets, one of which involves time-dependent covariates, are used to demonstrate the approach proposed. Simulation studies show that our two-step approach improves the kernel method proposed by Hoover and co-workers in several aspects such as accuracy, computational time and visual appeal of the estimators.

Original languageEnglish (US)
Pages (from-to)303-322
Number of pages20
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Functional analysis of variance
  • Functional linear models
  • Local polynomial smoothing
  • Longitudinal data analysis


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