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Dec 1998 Consistency of Bayes estimates for nonparametric regression: normal theory
Persi W. Diaconis, David Freedman
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Bernoulli 4(4): 411-444 (Dec 1998).


Performance characteristics of Bayes estimates are studied. More exactly, for each subject in a data set, let ξ be a vector of binary covariates and let Y be a normal response variable, with E{Y|ξ}=f(ξ) and var{Y|ξ}=1. Here, f is an unknown function to be estimated from the data; the subjects are independent and identically distributed. Define a prior distribution on f as kwkπk/∑kwk, where πk is standard normal on the set of f which only depend on the first k covariates and wk>0 for infinitely many k. Bayes estimates are consistent for all f. On the other hand, if the πk are flat, inconsistency is the rule.


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Persi W. Diaconis. David Freedman. "Consistency of Bayes estimates for nonparametric regression: normal theory." Bernoulli 4 (4) 411 - 444, Dec 1998.


Published: Dec 1998
First available in Project Euclid: 14 March 2007

zbMATH: 1037.62031
MathSciNet: MR1679791

Keywords: Bayes estimates , binary regression , consistency , Model selection

Rights: Copyright © 1998 Bernoulli Society for Mathematical Statistics and Probability

Vol.4 • No. 4 • Dec 1998
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