Mixtures of global and local edgeworth expansions and their applications

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Abstract

Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning variables are considered. The results are then applied to derive Edgeworth expansions for bootstrap distributions, for Bayesian bootstrap distribution, and for the distributions of statistics based on samples from finite populations. This results in a unified theory of Edgeworth expansions for resampling procedures. The Bayesian bootstrap is shown to be second order correct for smooth positive "priors," whenever the third cumulant of the "prior" is equal to the third power of its standard deviation. Similar results are established for weighted bootstrap when the weights are constructed from random variables with a lattice distribution.

Original languageEnglish (US)
Pages (from-to)282-307
Number of pages26
JournalJournal of Multivariate Analysis
Volume59
Issue number2
DOIs
StatePublished - Nov 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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