On a nonparametric resampling scheme for Markov random fields

Abstract

We study an extension to general Markov random fields of the resampling scheme given in Bickel and Levina (2006) [4] for texture synthesis with stationary Markov mesh models. The procedure generates bootstrap replicates of a sample using kernel regression and the principle of Gibbs sampling. Consistency of the bootstrap distribution is investigated under the Dobrushin contraction condition. Some simulation examples are given, in particular for the texture synthesis, for which the multiscale algorithm of Paget and Longstaff (1998) [27] is revisited.