On some class properties of statistical experiments under weak Blackwell equivalence (Q1192436)

The present paper discusses the connection between majorized statistical experiments and weak Blackwell equivalent experiments. Recall that an experiment \(E=(\Omega,{\mathcal A},\{P_ \theta:\theta\in\Theta\})\) is majorized if there exists a majorizing measure \(m\) such that each \(P_ \theta\) has an \(m\)-density. Majorization carries over to weakly Blackwell equivalent experiments \(F=(\Omega',{\mathcal A}',\{Q_ \theta:\theta\in\Theta\})\). Recall that by definition there exists a weak kernel \(N\) with \(Q_ \theta=\int N(x,\cdot)dP_ \theta(x)\), \(\theta\in\Theta\), and vice versa. The proof is based on the support criterion for majorization, see \textit{E. Torgersen}, Comparison of statistical experiments (1991; Zbl 0732.62009).