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Mixtures of Global and Local Edgeworth Expansions and Their Applications

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  • Babu, Gutti Jogesh
  • Bai, Z. D.
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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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 2 (November)
    Pages: 282-307

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:282-307

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    Related research

    Keywords: Asymptotic expansions Bayesian bootstrap bootstrap Chebyshev-Hermite polynomial Dirchlet distribution expansions for conditional distributions gamma distribution lattice distribution local limit theorems sampling without replacement weighted bootstrap;

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