Comparison of Experiments and Information Measures
Comparison of Experiments and Information Measures
Let $\mathscr{E}_x = \{X, S_X; P_\theta, \theta\in\Theta\}$ and $\mathscr{E}_Y = \{Y, S_Y; Q_\theta, \theta\in\Theta\}$ be two statistical experiments with the same parameter space $\Theta$. Some implications of the sufficiency of $\mathscr{E}_X$ for $\mathscr{E}_Y$, according to Blackwell's definition, are given in terms of Kullback-Leibler information and Fisher information matrices. For a …