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On Some Refinements of Jensen's Inequality

✍ Scribed by Mohammad Kazim Khan; Muhammad Hanif

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
268 KB
Volume
93
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper contains a link between Probability Proportional to Size (PPS) sampling and interpolations of the classical Jensen inequality. We show that these interpolating inequalities are, in fact, special cases of the conditional Jensen inequality when applied over an appropriate probability space. We provide a few examples dealing with divided differences, convex functions over linear spaces, approximation operators, and sampling with and without replacement.

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