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Mixtures of Global and Local Edgeworth Expansions and Their Applications

✍ Scribed by Gutti Jogesh Babu; Z.D. Bai

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
974 KB
Volume
59
Category
Article
ISSN
0047-259X

No coin nor oath required. For personal study only.

✦ Synopsis

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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