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2012 The asymptotic distribution of randomly weighted sums and self-normalized sums
Peter Kevei, David Mason
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Electron. J. Probab. 17: 1-21 (2012). DOI: 10.1214/EJP.v17-2092

Abstract

We consider the self-normalized sums $T_{n}=\sum_{i=1}^{n}X_{i}Y_{i}/\sum_{i=1}^{n}Y_{i}$, where $\{ Y_{i} : i\geq 1 \}$ are non-negative i.i.d.~random variables, and $\{ X_{i} : i\geq 1 \} $ are i.i.d. random variables, independent of $\{ Y_{i} : i \geq 1 \}$. The main result of the paper is that each subsequential limit law of $T_n$ is continuous for any non-degenerate $X_1$ with finite expectation, if and only if $Y_1$ is in the centered Feller class.

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Peter Kevei. David Mason. "The asymptotic distribution of randomly weighted sums and self-normalized sums." Electron. J. Probab. 17 1 - 21, 2012. https://doi.org/10.1214/EJP.v17-2092

Information

Accepted: 18 June 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.60028
MathSciNet: MR2946153
Digital Object Identifier: 10.1214/EJP.v17-2092

Subjects:
Primary: 60F05
Secondary: 60E07

JOURNAL ARTICLE
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Vol.17 • 2012
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