Summary
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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References
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Pitman, E. J. G. (1979).Some Basic Theory for Statistical Inference, Chapman and Hall, London.
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The Institute of Statistical Mathematics
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Kuboki, H. A generalization of the relative conditional expectatio—Further properties of Pitman'sT * and their applications to statistics. Ann Inst Stat Math 36, 181–197 (1984). https://doi.org/10.1007/BF02481963
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DOI: https://doi.org/10.1007/BF02481963