Efficient estimation for time-varying coefficient longitudinal models

• Published in: Journal of nonparametric statistics Vol. 30; no. 3; pp. 680 - 702
• Main Authors: Kim, Seonjin, Zhao, Zhibiao, Xiao, Zhijie
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.07.2018; Taylor & Francis Ltd
• Subjects: Asymptotic efficiency; bandwidth selection; Computer simulation; Covariance; Dependence; Fisher information; longitudinal model; Lower bounds; nonparametric smoothing; Nonparametric statistics; Optimization; Prewhitening; quantile regression; Quantiles; Regression analysis; time-varying coefficient
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2018.1467415

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.