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June, 1980 On the Limiting Behaviour of the Mode and Median of a Sum of Independent Random Variables
Peter Hall
Ann. Probab. 8(3): 419-430 (June, 1980). DOI: 10.1214/aop/1176994717

Abstract

Let $X_1, X_2, \cdots$ be independent and identically distributed random variables, and let $M_n$ and $m_n$ denote respectively the mode and median of $\Sigma^n_1X_i$. Assuming that $E(X^2_1) < \infty$ we obtain a number of limit theorems which describe the behaviour of $M_n$ and $m_n$ as $n \rightarrow \infty$. When $E|X_1|^3 < \infty$ our results specialize to those of Haldane (1942), but under considerably more general conditions.

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Peter Hall. "On the Limiting Behaviour of the Mode and Median of a Sum of Independent Random Variables." Ann. Probab. 8 (3) 419 - 430, June, 1980. https://doi.org/10.1214/aop/1176994717

Information

Published: June, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0442.60049
MathSciNet: MR573283
Digital Object Identifier: 10.1214/aop/1176994717

Subjects:
Primary: 60G50
Secondary: 60F99

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 3 • June, 1980
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