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Activity Number:
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378
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Type:
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Topic Contributed
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Date/Time:
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Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Stat. Sciences*
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| Abstract - #301429 |
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Title:
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Adaptive Nonparametric Estimation of Mean and Variance Functions
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Author(s):
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David Chan*+ and Robert Kohn and Chris Kirby
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Affiliation(s):
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CSIRO Mathematical and Information Sciences and University of New South Wales and Australian Graduate School of Management
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Address:
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Bldg E6B, Macquarie University, Sydney, International, 2122, Australia
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Keywords:
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Additive model ; Bayesian estimation ; Monte Carlo Markov Chain ; Radial basis functions ; Time series regression
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Abstract:
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We consider the estimation of a regression model with Gaussian errors, where both the mean and the variance are modeled as functions of the explanatory variables. A Bayesian approach is proposed to simultaneosuly estimate the mean and the variance functions, with the estimators being nonparametric and spatially adaptive. That is, the functional forms of the mean and variance are not assumed to be known, and both the mean and the variance functions can be smooth in one part of the space and wiggly in another part. In time series applications, we impose a boundary correction for the estimators of the mean and the variance functions to overcome bias. The whole model is estimated using a Markov chain simulation method that is specially constructed to integrate out the coefficients in the mean and to generate parameters and latent variables in blocks. This methodology is applied to a number of simulated and real examples and shown to work well.
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