ABSTRACT
Let X be a random variable taking values on a sample space X (usually X will be a subset of Rn, n-dimensional Euclidean space). Suppose that the distribution function F of X depends on a certain number of parameters, and
suppose further that the functional form of F is known except perhaps for a finite
number of these parameters; we denote by θ the vector of unknown parameters associated with F. Let (X , βX , Pθ)θ∈Θ be the statistical space associated with the random variable X, where βX is the σ-field of Borel subsets A ⊂ X and {Pθ}θ∈Θ a family of probability distributions defined on the measurable space (X , βX ) with Θ an open subset of RM0 , M0 ≥ 1. In the following the support of the probability distribution Pθ is denoted by SX .
