Wild bootstrap of the mean in the infinite variance case

Giuseppe Cavaliere, Iliyan Georgiev and Robert Taylor
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Iliyan Georgiev: Faculdade de Economia, Universidade Nova de Lisboa

No 5, Quaderni di Dipartimento from Department of Statistics, University of Bologna

Abstract: It is well known that the standard i.i.d. bootstrap of the mean is inconsistent in a location model with infinite variance (?-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the i.i.d. bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986, Ann.Stat.) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the i.i.d. bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods

Keywords: Bootstrap; distribuzioni stabili; misure di probabilità stocastiche; convergenza debole Bootstrap; stable distributions; random probability measures; weak convergence (search for similar items in EconPapers)
Pages: 15
Date: 2011
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