ABSTRACT

In this chapter, various applications of minimum distance methods to other scientific disciplines will be provided.

The minimum distance approach is widely used for estimating unknown target parameters from given data. Fundamentally, the axiom of a distance D on the set X consists of the following three conditions: D(x, y) ≥ 0 (nonnegativity), D(x, y) = D(y, x) (symmetry), and D(x, y) +D(y, z) ≥ D(x, z) (the triangle inequality) for all x, y, z ∈ X . The nonnegativity condition represents the consistency between two elements. We will consider “incomplete” distances satisfying the nonnegativity condition, where the measure is zero if and only if the arguments are identically equal. We have referred to such measures as statistical distances in previous chapters, which are widely used for estimating different target parameters.