Bayesian Statistics Seminar
North Carolina State University
presents
Changku Kang
North Carolina State University
"Regression via clustering using Dirichlet mixtures"
ABSTRACT
Regression problem is a popular method in modern statistics. If the underlying distribution X has unknown clusters, then the usual assumption, the homoscedasity may not be appropriate. In estimating the regression function, the suggested idea is that first it needs to find the clusters by the Dirichlet mixture and then use standard regression methods such as linear or polynomial. MCMC sampling method is used to find the clusters and at each sample the estimated regression functions can be obtained. We also apply our method to the large p, small n problem, where the number of variable p is much greater than the number of samples n. In several simulation works, this method is compared to other nonparametric methods such as kernel and smoothing spline in univariate case and GAM (generalized additive model) and MARS (Multivariate Adaptive Regression Splines) in multivariate case. The consistency issues is discussed without explicit proof.
Tuesday, August, 30, 2005
4:00 - 5:00 pm
208 Patterson Hall