7,918 research outputs found

    A Refinement of Jensen's Discrete Inequality for Differentiable Convex Functions

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    A refinement of Jensenā€™s discrete inequality and applications for the celebrated Arithmetic Mean ā€“ Geometric Mean ā€“ Harmonc Mean inequality and Cauchy-Schwartz-Bunikowski inequality are pointed out

    A Converse of the Jensen Inequality for Convex Mappings of Several Variables and Applications

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    In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and RĆ©nyi's entropy mappings are also given

    New results on mixture and exponential models by Orlicz spaces

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    New results and improvements in the study of nonparametric exponential and mixture models are proposed. In particular, different equivalent characterizations of maximal exponential models, in terms of open exponential arcs and Orlicz spaces, are given. Our theoretical results are supported by several examples and counterexamples and provide an answer to some open questions in the literature.Comment: Published at http://dx.doi.org/10.3150/15-BEJ698 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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