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Bayesian consistency for regression models under a supremum distance |
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| Authors: | Fei Xiang Stephen G. Walker |
| Affiliation: | 1. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK;2. School of Mathematics, Statistics and Actuarial Science, Cornwallis Building, University of Kent, Canterbury, Kent CT2 7NF, UK |
| Abstract: | This paper studies the consistency of Bayesian nonparametric regression models. We concentrate on the use of the sup metric and dealing with non-stochastic, i.e. designed, covariate values. We illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. |
| Keywords: | Bayesian nonparametric Consistency Regression model Hellinger neighborhood Piecewise constant function |
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