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
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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 $X$.
[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