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December, 1993 Nonparametric Binary Regression: A Bayesian Approach
P. Diaconis, D. A. Freedman
Ann. Statist. 21(4): 2108-2137 (December, 1993). DOI: 10.1214/aos/1176349413


The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let $\xi$ be a vector of binary covariates and let $\eta$ be a binary response variable, with $P\{\eta = 1\mid \xi\} = f(\xi)$. Here, $f$ is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural "balance" condition. Define a prior distribution on $f$ as $\sum_kw_k\pi_k/\sum_kw_k$, where $\pi_k$ is uniform on the set of $f$ which only depend on the first $k$ covariates and $w_k > 0$ for infinitely many $k$. Bayes estimates are consistent at all $f$ if $w_k$ decreases rapidly as $k$ increase. Otherwise, the estimates are inconsistent at $f \equiv 1/2$.


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P. Diaconis. D. A. Freedman. "Nonparametric Binary Regression: A Bayesian Approach." Ann. Statist. 21 (4) 2108 - 2137, December, 1993.


Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0797.62031
MathSciNet: MR1245784
Digital Object Identifier: 10.1214/aos/1176349413

Primary: 62A15
Secondary: 62E20

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 4 • December, 1993
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