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Consistency of the reduced bootstrap for sample means

Author

Listed:
  • Jiménez-Gamero, M.D.
  • Muñoz-García, J.
  • Cubiles-de-la-Vega, M.D.

Abstract

In this paper we consider the reduced bootstrap, that consists of only considering those bootstrap samples satisfying k1[less-than-or-equals, slant][nu]n[less-than-or-equals, slant]k2, for some 1[less-than-or-equals, slant]k1[less-than-or-equals, slant]k2[less-than-or-equals, slant]n, where [nu]n is the number of distinct original observations in the bootstrap sample. We show that, under mild conditions on k1 and k2, the reduced bootstrap estimator of the distribution of the sample mean is consistent. We also give conditions for it to be second order accurate and extend the obtained results to statistics that can be expressed as a smooth function of a multivariate sample mean and to their studentized versions.

Suggested Citation

  • Jiménez-Gamero, M.D. & Muñoz-García, J. & Cubiles-de-la-Vega, M.D., 2006. "Consistency of the reduced bootstrap for sample means," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 689-697, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:7:p:689-697
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    References listed on IDEAS

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    1. J. Munoz-Garcia & R. Pino-Mejias & J. M. Munoz-Pichardo & M. D. Cubiles-De-La-Vega, 1997. "Identification of outlier bootstrap samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(3), pages 333-342.
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    1. Jiménez Gamero, M. D. & Muñoz García, J. & Muñoz Reyes, A., 1998. "Bootstrapping statistical functionals," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 229-236, August.

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