Consistency of Bayes estimators of a binary regression function

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dc.creatorCoram, Marc
dc.creatorLalley, Steven P.
dc.date2004-12-10
dc.date2006-07-31
dc.date.accessioned2026-07-07T08:06:37Z
dc.date.available2026-07-07T08:06:37Z
dc.descriptionWhen do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let $ν$ be any probability distribution on the nonnegative integers. To sample a function $f$ from the prior $π^ν$, first sample $m$ from $ν$ and then sample $f$ uniformly from the set of step functions from $[0,1]$ into $[0,1]$ that have exactly $m$ jumps (i.e., sample all $m$ jump locations and $m+1$ function values independently and uniformly). The main result states that if a data-stream is generated according to any fixed, measurable binary-regression function $f_0\not\equiv1/2$, then frequentist consistency obtains: that is, for any $ν$ with infinite support, the posterior of $π^ν$ concentrates on any $L^1$ neighborhood of $f_0$. Solution of an associated large-deviations problem is central to the consistency proof.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053606000000236 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0412203
dc.identifierhttp://arxiv.org/abs/math/0412203
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 3, 1233-1269
dc.identifierdoi:10.1214/009053606000000236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130665
dc.subjectStatistics Theory
dc.subject62A15, 62E20 (Primary)
dc.titleConsistency of Bayes estimators of a binary regression function
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