Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T01:08:33.154Z Has data issue: false hasContentIssue false

On Goldstein’s variance bound

Published online by Cambridge University Press:  01 July 2016

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1985 

References

Agnew, R. A. (1972) Inequalities with applications in economic risk analysis. J. Appl. Prob. 9, 441444.Google Scholar
Goldstein, M. (1974) Some inequalities on variances. J. Appl. Prob. 11, 409412.Google Scholar
Gray, H. L. and Odell, P. L. (1967) On least favorable density functions. SIAM REV. 9, 715720.CrossRefGoogle Scholar
Jacobson, H. I. (1969) The maximum variance of restricted unimodal distributions. Ann. Math. Statist. 40, 17461752.Google Scholar
Miulwijk, J. (1966) Note on a theorem of M. N. Murthy and V. K. Sethi. Sankhya B 28, 183.Google Scholar
Seaman, J., Odell, P. and Young, D. (1985) Maximum variance unimodal distributions. Statist. Prob. Letters 3 (5).Google Scholar