Abstract
In this chapter we describe some of the asymptotic properties of Bayes procedures. These are obtained by using on the parameter set Θ a finite positive measure p and minimizing the average risk ∫ R (θ, ρ) μ (dθ). (See Chapter 2 for notation.) The procedure p that achieves this minimum will, of course, depend on the choice of μ. However, the literature contains numerous statements to the effect that, for large samples, the choice of μ matters little. This cannot be generally true, but we start with a proposition to this effect. If instead of μ one uses λ dominated by μ and if the density dλ/dp can be closely estimated, then a procedure that is nearly Bayes for p is also nearly Bayes for λ.
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© 2000 Springer Science+Business Media New York
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Le Cam, L., Yang, G.L. (2000). On Bayes Procedures. In: Asymptotics in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1166-2_8
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DOI: https://doi.org/10.1007/978-1-4612-1166-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7030-0
Online ISBN: 978-1-4612-1166-2
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