Estimating a Number of Cells via a Number of Occupied Ones under Random Choice

M. G. Chebunin<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: We consider a scheme of the series where support of the distribution and the sample size increase asymptotically proportionally. One knows a number of different elements of the sample only. We give consistent and asymptotically normal estimator of the parameter, defined as the limiting ratio of sample size to the number of elements of the support.

Keywords: number of different elements, a scheme of the series, consistency and asymptotic normality of the estimator.

UDC: 519.237.5

Received: 28.11.2013

 English version: Journal of Mathematical Sciences, 2016, 213:6, 795–801