Non-uniform bounds in local limit theorems in case of fractional moments. I

S. G. Bobkov; G. P. Chistyakov; F. Götze

doi:10.3103/S106653071103001X

Non-uniform bounds in local limit theorems in case of fractional moments. I

S. G. Bobkov
, G. P. Chistyakov
, F. Götze

School of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i. i. d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.

Original language	English (US)
Pages (from-to)	171-191
Number of pages	21
Journal	Mathematical Methods of Statistics
Volume	20
Issue number	3
DOIs	https://doi.org/10.3103/S106653071103001X
State	Published - Sep 2011

Bibliographical note

Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

Keywords

Edgeworth expansion
central limit theorem
fractional derivatives

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10.3103/S106653071103001X

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title = "Non-uniform bounds in local limit theorems in case of fractional moments. I",

abstract = "Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i. i. d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.",

keywords = "Edgeworth expansion, central limit theorem, fractional derivatives",

author = "Bobkov, \{S. G.\} and Chistyakov, \{G. P.\} and F. G{\"o}tze",

year = "2011",

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language = "English (US)",

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pages = "171--191",

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AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

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Y1 - 2011/9

N2 - Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i. i. d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.

AB - Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i. i. d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.

KW - Edgeworth expansion

KW - central limit theorem

KW - fractional derivatives

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UR - https://www.scopus.com/pages/publications/84859567857#tab=citedBy

U2 - 10.3103/S106653071103001X

DO - 10.3103/S106653071103001X

M3 - Article

AN - SCOPUS:84859567857

SN - 1066-5307

VL - 20

SP - 171

EP - 191

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

IS - 3

ER -

Non-uniform bounds in local limit theorems in case of fractional moments. I

Abstract

Bibliographical note

Keywords

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