On Estimation of Finite Population Proportion

TL;DR

This paper explores methods for estimating the proportion of a finite population, introducing explicit sample size formulas, inverse sampling schemes, and multistage procedures to ensure accuracy and confidence levels.

Contribution

It presents new formulas and schemes for finite population proportion estimation, including fixed sample size, inverse sampling, and multistage methods with guaranteed precision.

Findings

Derived explicit sample size formula for mixed error criteria

Established threshold determination for inverse sampling with relative precision

Developed multistage scheme for fixed-width confidence intervals with coverage guarantees

Abstract

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and relative errors. Second, we consider an inverse sampling scheme such that the sampling is continue until the number of units having a certain attribute reaches a threshold value or the whole population is examined. We have established a simple method to determine the threshold so that a prescribed relative precision is guaranteed. Finally, we develop a multistage sampling scheme for constructing fixed-width confidence interval for the proportion of a finite population. Powerful computational techniques are introduced to make it possible that the fixed-width confidence interval ensures prescribed level of coverage probability.