Efficient estimation for time-varying coefficient longitudinal models. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Kim, Seonjin; Zhao, Zhibiao; Xiao, Zhijie
• Is Part Of: Journal of nonparametric statistics. Volume 30:Issue 3(2018)
• Page Start: 680
• Page End: 702
• Publication Date: 2018-07-03
• Subjects: Asymptotic efficiency -- bandwidth selection -- Fisher information -- longitudinal model -- nonparametric smoothing -- prewhitening -- quantile regression -- time-varying coefficient; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2018.1467415
• Languages: English
• ISSNs: 1048-5252

Abstract

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.