The Admissibility of the Linear Interpolation Estimator of the Population Total

Abstract

Consider the problem of estimating the total of some finite population. Suppose the labels attached to the units of the population are such that members of the population whose labels are close together are more alike than units whose labels are far apart. For such a population a sensible estimator of the population total is one that interpolates linearly between successive members of the sample. The admissibility of this estimator will be demonstrated. The related interval estimators will be studied as well.