Division of Sample Information II: Likelihood Structure

Abstract

The definition of likelihood (2.1) and the subsequent development applies generally to a vector parameter θ = θ₁,..., θ _k In the examples discussed θ was a single scalar parameter or a vector parameter of two components. In the former case likelihood functions can be plotted and likelihood intervals, or the union of such intervals, obtained. In the latter case likelihood contours can be plotted and likelihood regions obtained. The difficulty in dealing with larger numbers of parameters is that of summarizing a three-dimensional or higher likelihood function. The problem is one of joint estimation-the estimation statements apply to all of the components of the parametric vector jointly.