Choosing data sets that optimize the determinant of the Fisher information matrix

Abstract

In many situations it is desirable to operate on a subset of the data only. These can arise in the areas of experimental design, robust estimation of multivariate location, and density estimation. The paper describes a method of subset selection that optimizes the determinant of the Fisher information matrix (FIM) which is called the effective independence distribution (EID) method. It provides some motivation that justifies the use of the EID, and the problem of finding the subset of points to use in the estimation of the minimum volume ellipsoid (MVE) is examined as an application of interest.