Nonasymptotic approach to Bayesian semiparametric inference

M. E. Panov

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The classical semiparametric Bernstein–von Mises (BvM) results is reconsidered in a non-classical setup allowing finite samples and model misspecication. We obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the target parameter and in the dimension of sieve approximation of the nuisance parameter. This helps to identify the so called critical dimension pn of the sieve approximation of the full parameter for which the BvM result is applicable. If the bias induced by sieve approximation is small and dimension of sieve approximation is smaller then critical dimension than the BvM result is valid. In the important i.i.d. and regression cases, we show that the condition “pn 2q/n is small”, where q is the dimension of the target parameter and n is the sample size, leads to the BvM result under general assumptions on the model.

    Original languageEnglish
    Pages (from-to)155-158
    Number of pages4
    JournalDoklady Mathematics
    Volume93
    Issue number2
    DOIs
    Publication statusPublished - 1 Mar 2016

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