Consistency of Bayesian estimation of a step function

Heng Lian

Statistics & Probability Letters, 2007, vol. 77, issue 1, 19-24

Abstract: We study in this paper the consistency of Bayesian estimation of a piecewise constant function defined on [0,1] with observations on a grid, using the method in Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536-561.] In particular, we show that consistency is achieved if the prior on the number of jumps is a Poisson distribution and the prior puts positive mass on the neighborhood of the true function.

Keywords: Nonparametric; Bayesian; estimation; Consistency; Piecewise; constant; function (search for similar items in EconPapers)
Date: 2007
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