Abstract Estimation of a closed population size (N) under inverse binomial sampling consists of four basic steps: First, one captures t items, then tag these t items, followed by releasing the t tagged items back to the population. Then, one draws items from the population one by one until s tagged items are recaptured where s is fixed in advance. In the recapturing stage (fourth step), items are normally drawn with replacement. But, without replacement, sampling will not be impacted much if N is large. Under squared error loss (SEL) as well as weighted SEL, we propose sequential methodologies to come up with bounded risk point estimators of an optimal choice of s, leading to an appropriate sequential estimator of N: The sequential estimation methodologies are supplemented with appropriate first-order asymptotic properties, followed by extensive data analyses.

中文翻译：

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在逆二项式抽样下，在重新捕获阶段顺序估计所需的最佳观察到的标记项的数量是有限的

摘要 逆二项式抽样下的封闭总体规模（N）的估计包括四个基本步骤：首先，捕获t个项目，然后标记这些t个项目，然后将t个标记的项目释放回总体。然后，一个人从总体中一一抽取项目，直到重新捕获 s 个标记的项目，其中 s 预先固定。在回收阶段（第四步），物品通常是有替换的。但是，在没有替换的情况下，如果 N 很大，采样不会受到太大影响。在平方误差损失 (SEL) 和加权 SEL 下，我们提出了顺序方法来提出 s 的最佳选择的有界风险点估计量，从而得到 N 的适当顺序估计量：顺序估计方法首先补充适当的-阶渐近性质，