On a problem of estimation of an infinite-dimensional parameter
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 187-203
Cet article a éte moissonné depuis la source Math-Net.Ru
Let $X$ be a random variable taking the positive integer values and let $\mathbf P\{X=k\}=\theta(k)$. We consider the problem of estimation of the parameter $\theta=(\theta(1),\theta(2),\dots)$ on the base of the sample $X_1,X_2,\dots,X_n$ where the observations $X_j$ are independent copies of $X$.
@article{ZNSL_2015_441_a11,
author = {V. A. Ershov and I. A. Ibragimov},
title = {On a~problem of estimation of an infinite-dimensional parameter},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {187--203},
year = {2015},
volume = {441},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a11/}
}
V. A. Ershov; I. A. Ibragimov. On a problem of estimation of an infinite-dimensional parameter. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 187-203. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a11/
[1] P. Billingsli, Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR
[2] U. Grenander, Abstract Inference, Wiley, New York, 1981 | MR | Zbl
[3] I. A. Ibragimov, R. Z. Khasminskii, Asimptoticheskaya teoriya otsenivaniya, Nauka, M., 1979 | MR
[4] V. V. Petrov, Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987 | MR
[5] R. Hasminskii, I. Ibragimov, “On density estimation in the view of Kolmogorov's ideas in approximation theory”, Ann. Statist., 18:3 (1990), 999–1010 | DOI | MR | Zbl