Efficient estimation for time-varying coefficient longitudinal models

Seonjin Kim, Zhibiao Zhao, Zhijie Xiao

Research output: Contribution to journalArticle

Abstract

For estimation of time-varying coefficient longitudinal models, the widely used local least-squares (LS) or covariance-weighted local LS smoothing uses information from the local sample average. Motivated by the fact that a combination of multiple quantiles provides a more complete picture of the distribution, we investigate quantile regression-based methods to improve efficiency by optimally combining information across quantiles. Under the working independence scenario, the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound. In the presence of dependence among within-subject measurements, we adopt a prewhitening technique to transform regression errors into independent innovations and show that the prewhitened optimally weighted quantile average estimator asymptotically achieves the Cramér–Rao bound for the independent innovations. Fully data-driven bandwidth selection and optimal weights estimation are implemented through a two-step procedure. Monte Carlo studies show that the proposed method delivers more robust and superior overall performance than that of the existing methods.

Original languageEnglish (US)
Pages (from-to)680-702
Number of pages23
JournalJournal of Nonparametric Statistics
Volume30
Issue number3
DOIs
StatePublished - Jul 3 2018

Fingerprint

Time-varying Coefficients
Efficient Estimation
Quantile
Least Squares
Estimator
Bandwidth Selection
Quantile Regression
Asymptotic Variance
Monte Carlo Study
Data-driven
Smoothing
Regression
Model
Transform
Lower bound
Scenarios
Efficient estimation
Time-varying coefficients
Innovation
Independent innovation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Efficient estimation for time-varying coefficient longitudinal models. / Kim, Seonjin; Zhao, Zhibiao; Xiao, Zhijie.

In: Journal of Nonparametric Statistics, Vol. 30, No. 3, 03.07.2018, p. 680-702.

Research output: Contribution to journalArticle

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