On Some Refinements of Jensenʹs Inequality Original Research Article

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.