Simultaneous Nonparametric Regression Analysis for Sparse Longitudinal Data

• Activity Number: 475
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Hongyuan Cao* and Weidong Liu and Zhou Zhou
• Companies: University of Missouri - Columbia and Shanghai Jiaotong University and University of Toronto
• Keywords: kernel smoothing ; maximum deviation ; nonparametric regression ; sparse longitudinal data ; simultaneous confidence band

Abstract

The paper considers simultaneous inference of time-varying coefficient models for sparse longitudinal data with time-invariant and time-variant covariates. The error and covariate processes are modelled as very general classes of non-Gaussian and non-stationary processes and are allowed to be cross-correlated. Simultaneous confidence bands (SCB) with asymptotically correct coverage probabilities are constructed to assess the overall pattern and magnitude of the time-varying association between the response and covariates. Our theoretical results shed light on the open problem of simultaneous inference of kernel nonparametric regression models for sparse longitudinal data. A simulation based method is proposed to overcome the problem of slow convergence of the asymptotic results. Simulation studies illustrate the advantages of our methodology over the existing point-wise and Bofferroni methods. Our methodology is applied to a longitudinal study of HIV infectious status.