Estimator Statistics from Simulation-Free Dirichlet Block-Bootstrap Resampling

Since the initiation of two variants of the bootstrap method by Efron and Rubin in the late 1970s, a variety of advancements has emerged in the literature. The subsampling of blocks enabled the estimation of the actual variance of the sample mean. The equivalence of the data-level and the estimator-level resampling is easily established for the sample mean and estimators alike. For Rubin’s variant of the bootstrap we apply an algorithm by Diniz et al. which allows for the numerically stable computation of the sample-based cumulative distribution function of the estimator under investigation. No actual Monte-Carlo resampling is necessary in this setting and we demonstrate how we get access to the very small probabilities of the tails and moreover to confidence intervals. We do this at the example of a well-known test model that exhibits geometrically decaying spatial correlations. The analysis naturally applies to temporally correlated systems or to the correlations occurring in Markov chains, as well.