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October, 1979 Estimation of a Convex Real Parameter of an Unknown Information Source
John C. Kieffer
Ann. Probab. 7(5): 882-886 (October, 1979). DOI: 10.1214/aop/1176994948

Abstract

Let $\mathscr{P}$ be the family of all stationary information sources with alphabet $A$. Let $F: \mathscr{P} \rightarrow(-\infty, \infty)$ be convex and upper semicontinuous in the weak topology. It is shown that for $n = 1,2, \cdots$, there is an estimator $Y_n: A^n \rightarrow (-\infty, \infty)$, such that if $\mu \in \mathscr{P}$ is ergodic and the process $(X_1, X_2,\cdots)$ has distribution $\mu$, then $Y_n(X_1,\cdots, X_n)\rightarrow F(\mu)$ in $L^1$ mean.

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John C. Kieffer. "Estimation of a Convex Real Parameter of an Unknown Information Source." Ann. Probab. 7 (5) 882 - 886, October, 1979. https://doi.org/10.1214/aop/1176994948

Information

Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0417.94006
MathSciNet: MR542139
Digital Object Identifier: 10.1214/aop/1176994948

Subjects:
Primary: 94A15
Secondary: 28A65 , 60G10

Keywords: Ergodic information source , sequence of estimators , upper-semicontinuous and convex function of a source , weak topology

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 5 • October, 1979
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