Deterministic bootstrapping for a class of bootstrap methods

03/26/2019

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by   Thomas Pitschel, et al.

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An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method T_n^*, alleviating the need for repeated resampling from observations (resp. input-derived data). In essence, the algorithm computes the distribution function from a linear mixture of independent random variables each having a finite discrete distribution. The algorithm is applicable to elementary bootstrap scenarios (targetting the mean as parameter of interest), for block bootstrap, as well as for certain residual bootstrap scenarios. Moreover, the algorithm promises a much broader applicability, in non-bootstrapped hypothesis testing.