Empirical likelihood semiparametric regression analysis for longitudinal data

Liugen Xue*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)

Abstract

A semiparametric regression model for longitudinal data is considered. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence regions and intervals. It is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made. Two calibrated empirical likelihood approaches to inference for the baseline function are developed. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence for the longitudinal semiparametric regression model, and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest. This leads us to prove a nonparametric version of Wilks' theorem. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation compares the empirical likelihood and normal-based methods in terms of coverage accuracies and average areas/lengths of confidence regions/intervals.

Original languageEnglish
Pages (from-to)921-937
Number of pages17
JournalBiometrika
Volume94
Issue number4
DOIs
Publication statusPublished - Dec 2007

Scopus Subject Areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Confidence region; Empirical likelihood
  • Longitudinal data
  • Maximum empirical likelihood estimator
  • Semiparametric regression model

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