Estimation of the size of a closed population

S. Sengupta¹

¹ Department of Statistics Calcutta University 35, Ballygunge Circular Road Kolkata 700019, India

Applicationes Mathematicae, Tome 37 (2010) no. 2, pp. 237-245

Résumé

The problem considered is that of estimation of the size $(N)$ of a closed population under three sampling schemes admitting unbiased estimation of $N$. It is proved that for each of these schemes, the uniformly minimum variance unbiased estimator (UMVUE) of $N$ is inadmissible under square error loss function. For the first scheme, the UMVUE is also the maximum likelihood estimator (MLE) of $N$. For the second scheme and a special case of the third, it is shown respectively that an MLE and an estimator which differs from an MLE by at most one have uniformly smaller mean square errors than the respective UMVUE's.

Détail

DOI : 10.4064/am37-2-8

Keywords: problem considered estimation size closed population under three sampling schemes admitting unbiased estimation proved each these schemes uniformly minimum variance unbiased estimator umvue inadmissible under square error loss function first scheme umvue maximum likelihood estimator mle second scheme special third shown respectively mle estimator which differs mle have uniformly smaller mean square errors respective umvues