Recent history functional linear models for sparse longitudinal data

Kion Kim, Damla Şentürk, Runze Li

Research output: Contribution to journalArticle

8 Citations (Scopus)

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
StatePublished - Apr 1 2011

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Functional Linear Model
Sparse Data
Longitudinal Data
Predictors
Uniform Consistency
Varying Coefficient Model
Confidence Bands
Sliding Window
Asymptotic distribution
Efficacy
Irregular
Simulation Study
Trajectory
Estimator
Trajectories
History
Longitudinal data
Methodology
Prediction
Demonstrate

All Science Journal Classification (ASJC) codes

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

Cite this

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Recent history functional linear models for sparse longitudinal data. / Kim, Kion; Şentürk, Damla; Li, Runze.

In: Journal of Statistical Planning and Inference, Vol. 141, No. 4, 01.04.2011, p. 1554-1566.

Research output: Contribution to journalArticle

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