Recent history functional linear models for sparse longitudinal data

Kion Kim, Damla Şentürk, Runze Li

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We consider the recent history functional linear models, relating a longitudinal response to a longitudinal predictor where the predictor process only in a sliding window into the recent past has an effect on the response value at the current time. We propose an estimation procedure for recent history functional linear models that is geared towards sparse longitudinal data, where the observation times across subjects are irregular and the total number of measurements per subject is small. The proposed estimation procedure builds upon recent developments in literature for estimation of functional linear models with sparse data and utilizes connections between the recent history functional linear models and varying coefficient models. We establish uniform consistency of the proposed estimators, propose prediction of the response trajectories and derive their asymptotic distribution leading to asymptotic point-wise confidence bands. We include a real data application and simulation studies to demonstrate the efficacy of the proposed methodology.

Original languageEnglish (US)
Pages (from-to)1554-1566
Number of pages13
JournalJournal of Statistical Planning and Inference
Volume141
Issue number4
DOIs
Publication statusPublished - Apr 1 2011

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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