Minimum risk point estimation of the size of a finite population under mark–recapture strategy

Abstract

In this article, we address the problem of minimum risk point estimation for the size of a closed population using the weighted squared error loss function with a penalty of cost for each observation under the well-known mark–recapture strategy. In order to achieve minimum risk, a crucial point is to determine the number of items to obtain in the recapture phase. We first develop a purely sequential sampling scheme that will require much less sampling operations without losing accuracy of the estimation. Then, we develop a novel practical accelerated sequential method that will further accelerate the whole recapture process when sampling can be easily done in batches. The stopping rules of both purely sequential and accelerated sequential sampling schemes possess desirable asymptotic properties. All theoretical findings are double validated by extensive data analyses.