Uniform Strong Consistency of Rao-Blackwell Distribution Function Estimators
O'Reilly, Federico J. ; Quesenberry, C. P.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 1678-1679 / Harvested from Project Euclid
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In the independent sampling model, Rao-Blackwell distribution function estimators $\tilde{F}_n(x)$ obtained by conditioning on sufficient statistics $T_n(X_1, \cdots, X_n)$ are considered. If for each $n \geqq 1, T_n$ is symmetric in $X_1,\cdots, X_n$ and $T_{n+1}$ is $\mathscr{B}(T_n, X_{n+1})$ measurable, it is shown that $\tilde{F}_n(x)$ converges strongly to the corresponding $F(x)$ and uniformly in $x$. This is a direct generalization of the Glivenko-Cantelli theorem.
Publié le : 1972-10-14
Classification:  
@article{1177692401,
     author = {O'Reilly, Federico J. and Quesenberry, C. P.},
     title = {Uniform Strong Consistency of Rao-Blackwell Distribution Function Estimators},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 1678-1679},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692401}
}

O'Reilly, Federico J.; Quesenberry, C. P. Uniform Strong Consistency of Rao-Blackwell Distribution Function Estimators. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  1678-1679. http://gdmltest.u-ga.fr/item/1177692401/