Nonparametric Modelling of the Covariance Structures

Speaker: Dr. Huajun Ye, UIC

Time: 3.30pm-4.00pm, Nov 16 (Wednesday), 2011

Venue: E304

Abstract:

When nonparametric modelling longitudinal data smoothing splines specify work- ing covariance structures. Although asymptotically consistent when using arbitrary working covariance structures, the smoothing splines have the smallest variances when assuming the true covariance structures (Lin, et al. 2004). In this paper we parameterize the mean and co- variance nonparametric regression functions with piecewise quadratic splines (Ruppert, et al. 2003), and provide smooth estimates of the mean and covariance regression functions through maximizing the penalized likelihood based on a mixed model approach. We illustrate the pro- posed approach via analyzing two well-known data sets, the Cattle data (Kenward,1987) and the CD4+ cell data (Diggle, et al. 1994). A small simulation study is conducted to evaluate the efficacy of the method.