MONDAY, February 23, 2004
Time: 1:30 - 2:30 PM
Room BAL 239

Jeonggang (Martin) Seo
Department of Statistics
Purdue University
West Lafayette, IN 47907-2067

In a longitudinal marginal model with time-varying covariates, the local polynomial kernel smoothing method has the odd property that it performs better with entirely ignoring the correlation structure rather than correctly specifying the true covariance. In fact, the local behavior of the usual kernel method makes it difficult to use the correlations. Consequently, it can be substantially inferior to the Splines in terms of MSE. I will present a new kernel-based method that makes use of the correlation structure inherent in longitudinal data.

For the second part of the talk, I will describe two Bayesian nonparametric regression methods using local polynomial smoothing. The first method will be built on the famous Dirichlet Mixtures of normals. There are some interesting characteristics associated with the Dirichlet Process Prior in this particular context, which include unbalanced cluster formation. Investigating the allocation of observations induced by the Polya Urn characterization of the Dirichlet Process leads to the second method. This prior structure can be viewed as an extension of the Dirichlet Multinomial Allocation. These methods are easily extended to apply for multivariate models including the longitudinal model of interest. Some simulation results will be given to show that these Bayesian methods naturally utilize the correlation structures in longitudinal data and their performance is comparable to the Splines