Theory of Statistical Inference and Information

A-distance a-test Analogically assertion assumptions asymptotic Bayes Blackwell sufficient Borel subsets bounded conditional probability convex functions convex set Corollary countable Csiszár defined definition denote density differentiable distance dominated entropy estimation model Example exists f is strictly f-divergence F-measurable f-projection F₁ finite follows from Proposition function f Halmos holds implies inequality integral least favourable pair Lemma Let f Let us consider Liese and Vajda likelihood ratio likelihood ratio test limsup lower semicontinuous M-estimator mapping Markov kernel measurable space metric space minimizes nonempty nonnegative numbers o-algebra of Borel o-finite measure P₁ P₂ parameter probability measures Proof prove Q₁ Q₂ Radon-Nikodym derivative random variables regular conditional restriction satisfies the relation sequence signed measure statistical experiments strictly convex sub-o-algebra T₁ Theorem theory tion topology unique v₁ x₁ θε Θ θεΘ