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φ PHI-divergences, sufficiency, Bayes sufficiency, and deficiency

Friedrich Liese (2012)

Kybernetika

The paper studies the relations between φ -divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of φ -divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary...

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