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

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Valladolid, Valladolid, Spain

    Eustasio del Barrio & Carlos Matrán

  2. Mathematisches Institut, Heinrich-Heine Universität, Düsseldorf, Germany

    Arnold Janssen

Authors
  1. Eustasio del Barrio
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  2. Arnold Janssen
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  3. Carlos Matrán
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Corresponding author

Correspondence to Eustasio del Barrio.

Additional information

The authors have been partially supported by the Spanish Ministerio de Educación y Ciencia and FEDER, grant MTM2005-08519-C02-01,02 and the Consejería de Educación y Cultura de la Junta de Castilla y León, grant PAPIJCL VA102A06.

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del Barrio, E., Janssen, A. & Matrán, C. On the low intensity bootstrap for triangular arrays of independent identically distributed random variables. TEST 18, 283–301 (2009). https://doi.org/10.1007/s11749-007-0077-3

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  • DOI: https://doi.org/10.1007/s11749-007-0077-3

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