On the low intensity bootstrap for triangular arrays of independent identically distributed random variables

Autores: Eustasio del Barrio , Arnold Janssen, Carlos Matrán Bea
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 18, Nº. 2, 2009, págs. 283-301
Idioma: inglés
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Resumen
- In this work, we give a complete picture of the behavior of the low intensity bootstrap of linear statistics. Our setup is given by triangular arrays of independent identically distributed random variables and different normalizations related to the rates of bootstrap intensities. We show that the behavior of this low intensity bootstrap coincides with that of partial sums of a number of summands equal to the bootstrap resampling size. Agreement on the limit laws for different (small) bootstrap sizes is thus shown to be closely related to domains of attraction of α-stable laws. As a byproduct, we obtain local distributional properties of Lévy processes.