1. What have the authors contributed in "The fast iterated bootstrap" ?
In this paper, the authors extend the fast double bootstrap of Davidson and MacKinnon ( 2007 ) to higher orders of iteration, and provide algorithms for their implementation.. In a series of simulation experiments, the authors show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suffers from less size distortion under the null with no accompanying loss of power.
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2. What are the future works in "The fast iterated bootstrap" ?
The approximations that led to the fast double bootstrap have been extended not only to a fast triple bootstrap but to arbitrary levels of bootstrap iteration.. The authors hope to clarify these and other points in future work.. When the assumption of approximate independence does not hold, the bootstrap can be expected to perform badly ; see Davidson ( 2016b ).. With resampling, the authors know that it can not be, since, with repeated resampling, eventually a stage is reached in which only one element is resampled.
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