Theory of Statistical Inference and Information

a-test Analogically assertion asymptotic Bayes Blackwell sufficient Borel subsets bounded coincides conditional probability convex functions convex set Corollary countable Csiszár defined definition denote density differentiable distance dominated entropy equivalent estimation model Example exists f-divergence F-measurable f-projection finite follows from Proposition formula function f ƒ is strictly Halmos holds implies inequality integral least favourable pair Lemma Let us consider Liese and Vajda likelihood ratio likelihood ratio tests limsup lower semicontinuous M-estimator mapping Markov kernel measurable space metric space minimizes nonempty nonnegative numbers o-algebra of Borel o-finite measures obtains P₁ P₂ parameter probability measures Proof prove Q₁ R-distance Radon-Nikodym Radon-Nikodym derivative random variables regular conditional restriction result satisfies the relation sequence signed measure statistical experiments strictly convex sub-o-algebra T₁ Theorem theory tion topology unique v₁ x₁ Y₁ αμ