Semiparametric longitudinal model with irregular time autoregressive error process

Yang Bai, Jian Huang, Rui Li, Jinhong You

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)


This paper considers semiparametric inference for longitudinal data collected at irregular and possibly subject-specific times. We propose an irregular time autoregressive model for the error process in a partially linear model and develop a unified semiparametric profiling approach to estimating the regression parameters and autoregressive coefficients. An appealing feature of the proposed method is that it can effectively accommodate irregular and subject-specific observation times. We establish the asymptotic normality of the proposed estimators and derive explicit forms of their asymptotic variances. For the nonparametric component, we construct a two-stage local polynomial estimator. Our method takes into account the autoregressive error structure and does not drop any observations. The asymptotic bias and variance of the estimator are derived. We report on simulation studies conducted to evaluate the finite sample performance of the proposed method. The analysis of a dataset of CD4 cell counts of HIV seroconverters demonstrates its application.

Original languageEnglish
Pages (from-to)507-527
Number of pages21
JournalStatistica Sinica
Issue number2
Publication statusPublished - 1 Apr 2015
Externally publishedYes


  • Asymptotic normality
  • Irregular and subject-specific observation times
  • Locally linear estimation
  • Nonstationary autoregressive process
  • Profile least squares

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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