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.

摘要

在本文中，我们使用加权平方误差损失函数来解决封闭种群规模的最小风险点估计问题，并在众所周知的标记-重新捕获策略下对每个观察值进行代价惩罚。为了达到最小的风险，一个关键点是确定在重新捕获阶段要获得的物品数量。我们首先开发了一个纯粹的顺序采样方案，它将需要更少的采样操作而不会损失估计的准确性。然后，我们开发了一种新颖实用的加速顺序方法，当可以轻松地批量进行采样时，该方法将进一步加速整个重新捕获过程。纯顺序和加速顺序采样方案的停止规则都具有理想的渐近特性。