A Note on Random Sums with Nonrandom Centering

P. S. Griffin

doi:10.1023/A:1022608415953

A Note on Random Sums with Nonrandom Centering

P. S. Griffin

Department of Mathematics

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

1 Scopus citations

Abstract

Let X₁, X₂,... be a sequence of i.i.d. random variables and N_n a sequence ot nonnegative integer valued random variables, independent of {X_i}. The main results concern tightness and weak convergence of (A₁, + ... + X_Nn-nμ) γ_n¹ under the natural condition that the sample mean is a consistent estimator of μ.

Original language	English (US)
Pages (from-to)	333-348
Number of pages	16
Journal	Journal of Theoretical Probability
Volume	10
Issue number	2
DOIs	https://doi.org/10.1023/A:1022608415953
State	Published - 1997

Keywords

Domain of attraction
Nonrandom centering
Random sum
Tightness
Weak convergence

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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title = "A Note on Random Sums with Nonrandom Centering",

abstract = "Let X1, X2,... be a sequence of i.i.d. random variables and Nn a sequence ot nonnegative integer valued random variables, independent of {Xi}. The main results concern tightness and weak convergence of (A1, + ... + XNn-nμ) γn1 under the natural condition that the sample mean is a consistent estimator of μ.",

keywords = "Domain of attraction, Nonrandom centering, Random sum, Tightness, Weak convergence",

author = "Griffin, {P. S.}",

note = "Funding Information: Received May 26. 1995. 2Department of Mathematics, Syracuse University, Syracuse, New York Research supported by the NSA through a grant to Syracuse University.",

year = "1997",

doi = "10.1023/A:1022608415953",

language = "English (US)",

volume = "10",

pages = "333--348",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

publisher = "Springer New York",

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T1 - A Note on Random Sums with Nonrandom Centering

AU - Griffin, P. S.

N1 - Funding Information: Received May 26. 1995. 2Department of Mathematics, Syracuse University, Syracuse, New York Research supported by the NSA through a grant to Syracuse University.

PY - 1997

Y1 - 1997

N2 - Let X1, X2,... be a sequence of i.i.d. random variables and Nn a sequence ot nonnegative integer valued random variables, independent of {Xi}. The main results concern tightness and weak convergence of (A1, + ... + XNn-nμ) γn1 under the natural condition that the sample mean is a consistent estimator of μ.

AB - Let X1, X2,... be a sequence of i.i.d. random variables and Nn a sequence ot nonnegative integer valued random variables, independent of {Xi}. The main results concern tightness and weak convergence of (A1, + ... + XNn-nμ) γn1 under the natural condition that the sample mean is a consistent estimator of μ.

KW - Domain of attraction

KW - Nonrandom centering

KW - Random sum

KW - Tightness

KW - Weak convergence

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DO - 10.1023/A:1022608415953

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EP - 348

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 2

ER -

A Note on Random Sums with Nonrandom Centering

Abstract

Keywords

ASJC Scopus subject areas

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