Sequentially estimating the required optimal observed number of tagged items with bounded risk in the recapture phase under inverse binomial sampling

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.