Abstract
In this paper, we consider the estimation problem of the population density of organisms in an area. We formulate this biometric problem as a variant of the sequential estimation problem of the intensity of the Poisson process and propose a method for simultaneously optimizing both the decision of an observation subarea and the estimation. By request from the application side, we define the equivariance of a procedure composed of a decision rule of an observation subarea and an estimator of population density under the scale transformations of an observation area, and then construct a scale-equivariant procedure. As a result of using the invariance principle, we utilize the framework of statistical decision theory, not the conventional framework of sequential estimation using asymptotic methods, and discuss the admissibility and minimaxity of our proposed procedure.
