Concentration inequalities and limit theorems for randomized sums

Sergey G. Bobkov; Friedrich Götze

doi:10.1007/s00440-006-0500-9

Concentration inequalities and limit theorems for randomized sums

Sergey G. Bobkov, Friedrich Götze

School of Mathematics

Research output: Contribution to journal › Review article › peer-review

19 Scopus citations

Abstract

Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.

Original language	English (US)
Pages (from-to)	49-81
Number of pages	33
Journal	Probability Theory and Related Fields
Volume	137
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-006-0500-9
State	Published - Jan 1 2007

Keywords

Central limit theorem
Concentration
Orthogonal polynomials
Pairwise independent random variables
Self-normalized statistics
Typical distributions

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10.1007/s00440-006-0500-9

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title = "Concentration inequalities and limit theorems for randomized sums",

abstract = "Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.",

keywords = "Central limit theorem, Concentration, Orthogonal polynomials, Pairwise independent random variables, Self-normalized statistics, Typical distributions",

author = "Bobkov, {Sergey G.} and Friedrich G{\"o}tze",

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AU - Bobkov, Sergey G.

AU - Götze, Friedrich

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N2 - Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.

AB - Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.

KW - Central limit theorem

KW - Concentration

KW - Orthogonal polynomials

KW - Pairwise independent random variables

KW - Self-normalized statistics

KW - Typical distributions

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DO - 10.1007/s00440-006-0500-9

M3 - Review article

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SN - 0178-8051

VL - 137

SP - 49

EP - 81

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

Concentration inequalities and limit theorems for randomized sums

Abstract

Keywords

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