7,918 research outputs found
A Refinement of Jensen's Discrete Inequality for Differentiable Convex Functions
A refinement of Jensenās 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
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
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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