Abstract
This paper is concerned with the mappingT * which is a generalization of the relative conditional expectation. It has been introduced by E.J.G. Pitman (1979,Some Basic Theory for Statistical Inference, Chapman and Hall). First we extend the definition of the mappingT * and describe its fundamental properties. Moreover, we establish inequalities for convex functions with respect toT *. The mappingT * is very useful in analysing quantities associated with the distribution of a statisticT. The application of the mappingT * to statistics is another interest of this paper.
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