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On Goldstein’s variance bound

Published online by Cambridge University Press:  01 July 2016

John Seaman  and
Pat Odell
John Seaman*
Affiliation:
Baylor University
Pat Odell*
Affiliation:
University of Texas at Dallas
*
∗Postal address: Department of Information Systems, Hankamer School of Business, Baylor University, Waco, TX 76798, USA.
∗∗Postal address: Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA.
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Abstract

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Goldstein (1974) derived an upper bound on the variance of certain non-negative functions when the first two moments of the underlying random variable are known. This bound is compared to a simple and fundamental variance bound which requires only that the range of the function be known. It is shown that Goldstein’s bound frequently exceeds the simpler bound. Finally, an interpretation of such bounds in the context of economic risk analysis is given.

Keywords

VARIANCEINEQUALITYUPPER BOUNDSECONOMIC RISK ANALYSIS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 17 , Issue 3 , September 1985 , pp. 679 - 681
Copyright
Copyright © Applied Probability Trust 1985 

References

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