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Rao-Blackwellisation of sampling schemes. (English) Zbl 0866.62024
Summary: This paper proposes a post-simulation improvement for two common Monte Carlo methods, the Accept-Reject and Metropolis algorithms. The improvement is based on a Rao-Blackwellisation method that integrates over the uniform random variables involved in the algorithms, and thus post-processes the standard estimators. We show how the Rao-Blackwellised versions of these algorithms can be implemented and, through examples, illustrate the improvement in variance brought by these new procedures. We also compare the improved version of the Metropolis algorithm with ordinary and Rao-Blackwellised importance sampling procedures for independent and general Metropolis set-ups.

62G99Nonparametric inference
62D05Statistical sampling theory, sample surveys
62G05Nonparametric estimation