u(\boldsymbol{\theta}) \in \Psi \subseteq
\mathbb{R}\). Given a sample of size \(n\) from \(\boldsymbol{T}\), say
\(\boldsymbol{X} = (X_1, \ldots, X_k)\), which is a vector of counts obtained
by concatenating the k independent count vectors, let \(G(\boldsymbol{X})\)
denote a real-valued statistic that defines the ordering of the sample space.
The default choice of the statistic is to estimate \(\boldsymbol{\theta}\)
with the sample proportions and plug them into \(\tau(\boldsymbol{\theta})\).
This function