Geodesic
On the estimation of the size of a~finite population
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 380-384

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We construct some estimates of the unknown size $N$ of finite population which are based on the sample of size $n$ drawn with replacement from this population. For the case when $N$, $n\to\infty$ and $0\alpha_1\le \alpha=\frac{n}{N}\le\alpha_2\infty$ (where $\alpha_1$ and $\alpha_2$ are given constants) a class of consistent uniformly asymptotically normal estimates of the parameter $\alpha$ is introduced. An asymptotically optimal (in this class) estimate is shown to be a function of the number $\eta_n$ of different elements in the sample. 
@article{TVP_1982_27_2_a22,
     author = {G. I. Iv\v{c}enko and E. E. Timonina},
     title = {On the estimation of the size of a~finite population},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {380--384},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a22/}
}
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G. I. Ivčenko; E. E. Timonina. On the estimation of the size of a~finite population. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 380-384. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a22/