Estimation of the size of a closed population

Volume 37 / 2010

S. Sengupta Applicationes Mathematicae 37 (2010), 237-245 MSC: 62D05, 62F10. DOI: 10.4064/am37-2-8


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.


  • S. SenguptaDepartment of Statistics
    Calcutta University
    35, Ballygunge Circular Road
    Kolkata 700019, India

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