The Cuboid as Parameter Space

Abstract

In this chapter we consider the cuboid

$$\otimes = \left\{ {\theta \in \mathbb{R}^N :0 \leqslant y_\text{i} \leqslant x_i \,;\,i = 1, \ldots N} \right\}$$

as parameter space, where the x_i’s are known positive real numbers. Typical situations for θ are given if x_i denotes the numbers of secondary units in the i- th primary unit. For example, let x_i be the size of household i and y_i the number of its members who are struck with a certain disease. Frequently all x_i are equal. In a test it is possible to obtain 0,1,…,40 points. y_i then would be the number of points which the i- th participant of the test obtains.