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This paper proposes a new sharpened version of the Jensens inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form. Applications to the moment generating function, power mean inequalities, and Rao-Blackwell estimation are presented. This presentation can be incorporated in any calculus-based statistical course.
We establish Bernstein inequalities for functions of general (general-state-space, not necessarily reversible) Markov chains. These inequalities achieve sharp variance proxies and recover the classical Bernsteins inequality under independence. The ke
A real valued function defined on}$mathbb{R}$ {small is called}$g${small --convex if it satisfies the following textquotedblleft generalized Jensens inequalitytextquotedblright under a given}$g${small -expectation, i.e., }$h(mathbb{E}^{g}[X])leq math
We extend Fanos inequality, which controls the average probability of events in terms of the average of some $f$--divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary $[0,1]$--valued random variable
Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (e.g., Gaussian). For the corresponding limit experiment, we characterize the frequentist size of a certain Ba
Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.