A sharp inequality for the -center of gravity of a random variable
David C. Cox
Proc. Amer. Math. Soc. 93 (1985), 106-110
Primary 60E15; Secondary 44A60
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Abstract: Let be a real-valued random variable. For , define the -center of gravity of , , as the unique number which minimizes . This paper exhibits a more-or-less explicit expression for the best constant in the inequality , and presents asymptotic formulas for as and , respectively. The definition of is extended to variables taking values in an arbitrary Hilbert space , and it is shown that is not increased by this extension.
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- E. Hewitt and K. Stromberg, Real and abstract analysis, Grad. Texts in Math., Vol. 25, Springer-Verlag, New York, 1975. MR 0367121 (51:3363)
- J. H. B. Kemperman, The general moment problem, a geometric approach, Ann. Statist. 39 (1968), 93-122. MR 0247645 (40:909)
- F. W. J. Olver, Asymptotics and special functions, Academic Press, New York, 1974. MR 0435697 (55:8655)
- H. S. Witsenhausen, On performance bounds for uncertain systems, SIAM J. Control Optim. 8 (1970), 55-89. MR 0273738 (42:8615)
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