Translator Disclaimer
April, 1980 Precision Bounds for the Relative Error in the Approximation of $E|S_n|$ and Extensions
Michael J. Klass
Ann. Probab. 8(2): 350-367 (April, 1980). DOI: 10.1214/aop/1176994782

Abstract

Let $S_n$ denote the $n$th partial sum of i.i.d. nonconstant mean zero random variables. Given an approximation $K(n)$ of $E|S_n|$, tight bounds are obtained for the ratio $E|S_n|/K(n)$. These bounds are best possible as $n$ tends to infinity. Implications of this result relate to the law of the iterated logarithm for mean zero variables, Chebyshev's inequality and Markov's inequality. Asymptotically exact lower-bounds are obtained for expectations of functions of row-sums of triangular arrays of independent but not necessarily identically distributed random variables. Expectations of "Poissonized random sums" are also treated.

Citation

Download Citation

Michael J. Klass. "Precision Bounds for the Relative Error in the Approximation of $E|S_n|$ and Extensions." Ann. Probab. 8 (2) 350 - 367, April, 1980. https://doi.org/10.1214/aop/1176994782

Information

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

zbMATH: 0428.60058
MathSciNet: MR566599
Digital Object Identifier: 10.1214/aop/1176994782

Subjects:
Primary: 60G50
Secondary: 26A86, 60E05

Rights: Copyright © 1980 Institute of Mathematical Statistics

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.8 • No. 2 • April, 1980
Back to Top