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The stochastic geyser problem for sample quantiles

Published online by Cambridge University Press:  14 July 2016

Stephen A. Book
Stephen A. Book*
Affiliation:
California State College, Dominguez Hills
*
∗Postal address: Department of Mathematics, California State College, Dominguez Hills, 1000 East Victoria St., Dominguez Hills, CA 90747, U.S.A.
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Abstract

Consider a sequence of observations Yk = Xk + ek, where {Xk : 1 ≦ k < ∞} are i.i.d. random variables having distribution function F and {ek : 1 ≦ k < ∞} are arbitrary random errors of observation. The stochastic geyser problem asks for conditions under which F can be uniquely determined from a knowledge of the sequence of Yk's. The objective of the present article is to show that, if F is continuous and strictly increasing and the sample quantiles of successive blocks {Xn+ 1Xn+ 2, …, Xn+ K} of particular lengths K can be a.s. estimated to within an error of size o(1) as K →∞, then we can almost surely determine F from a single realization of {Yk : 1 ≦ k < ∞}.

Keywords

ORDER STATISTICSERDÖS-RÉNYI STRONG LAWSTOCHASTIC GEYSER PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 445 - 448
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Research conducted while the author was visiting the University of California, Irvine, on sabbatical leave from California State College.

References

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