On continuity of the Bayes response (Corresp.)

In a statistical decision problem, the use of approximate or estimated priors leads naturally to the question of the continuity of risk <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R(θ, dG)</tex> in the variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> . This continuity condition is explored, and in the finite parameter state case, a characterization in terms of the differentiability of the Bayes envelope is given.