Abstract #301366

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JSM 2003 Abstract #301366
Activity Number: 399
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301366
Title: Estimation and Variable Selection in Nonparametric Heteroscedastic Models
Author(s): Robert Kohn*+ and Paul Yau
Companies: University of New South Wales and Australian Graduate School of Management
Address: Australian Graduate School of Management, Sydney 2052, , , Australia
Keywords: Bayesian analysis ; Markov chain Monte Carlo ; Penalized splines ; variance function estimation
Abstract:

A regression model with heteroscedastic errors, that is, errors whose variance is not constant, is considered. A Bayesian approach is used for simultaneously estimating the mean and variance functions of the regression model nonparametrically. The mean regression function is modeled by a polynomial spline or a radial basis with smoothing performed through knot selection. The variance regression function is also modeled by a polynomial spline or a radial basis function, but smoothing is carried out using a shrinkage approach, also known as a penalized likelihood approach. A method for selecting significant variables in both the mean and the variance functions is provided. The same methodology uses model averaging to overcome the problem of model uncertainty, that is determining which combination of variables enter the model.

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