A statistic using the concept of order - weighted information energy introduced by Tuteja et al. (1992) is considered and its asymptotic distribution in a stratified random sampling is obtained. Some special cases are also discussed.
Some basic results about invariance are given using quotient σ-fields. A strong kind of invariance is considered. Under appropriate conditions we obtain a sufficient statistics for models with such an invariance property.
We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer n such that μ*n is stochastically dominated by ν*n for two given probability measures μ and ν. As a consequence we obtain a similar theorem on the majorization order for vectors in Rd. In particular we prove results about catalysis in quantum information theory.
We consider some fundamental concepts of mathematical statistics in the Bayesian setting. Sufficiency, prediction sufficiency and freedom can be treated as special cases of conditional independence. We give purely probabilistic proofs of the Basu theorem and related facts.