An alternative to the m out of n bootstrap

Hemant Ishwaran, Lancelot F. James, Mahmoud Zarepour

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


It is well known that Efron's bootstrap can fail in settings where the data are heavy tailed and when regularity conditions do not hold. Naturally this applies to weighted bootstrap schemes such as the Bayesian bootstrap. To deal with this, we introduce a Bayesian bootstrap analogue of the m out of n bootstrap. This bootstrap differs from traditional m out of n bootstraps in that all n observations are used in the bootstrap test statistic. Moreover, the method is relatively robust to the selection of m. We establish consistency for the new bootstrap and examine its other useful properties including a connection to the Dirichlet process. Several examples illustrating consistency in settings where the Efron bootstrap fails are given. Further generalizations are suggested.

Original languageEnglish (US)
Pages (from-to)788-801
Number of pages14
JournalJournal of Statistical Planning and Inference
Issue number3
StatePublished - Mar 1 2009
Externally publishedYes


  • Bayesian bootstrap
  • Dirichlet process
  • Point process
  • Stable process
  • Sub-sampling

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability


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