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

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

doi:10.3103/S1066530711040016

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

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

School of Mathematics

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

3 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)	269-287
Number of pages	19
Journal	Mathematical Methods of Statistics
Volume	20
Issue number	4
DOIs	https://doi.org/10.3103/S1066530711040016
State	Published - Dec 2011

Bibliographical note

Funding Information:
Research was partially supported by NSF grant and SFB 701.

Keywords

Edgeworth expansion
central limit theorem
fractional derivatives

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10.3103/S1066530711040016

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

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",

note = "Funding Information: Research was partially supported by NSF grant and SFB 701.",

year = "2011",

month = dec,

doi = "10.3103/S1066530711040016",

language = "English (US)",

volume = "20",

pages = "269--287",

journal = "Mathematical Methods of Statistics",

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AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

N1 - Funding Information: Research was partially supported by NSF grant and SFB 701.

PY - 2011/12

Y1 - 2011/12

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

Abstract

Bibliographical note

Keywords

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