Estimation of a Convex Real Parameter of an Unknown Information Source

Kieffer, John C.

Ann. Probab., Tome 7 (1979) no. 6, p. 882-886 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1979-10-14
Classification:  Ergodic information source,  upper-semicontinuous and convex function of a source,  sequence of estimators,  weak topology,  94A15,  60G10,  28A65