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 μ and minimizing the average risk \(\int R(\theta,\rho)\mu(d\theta)\). (See Chapter 2 for notation). The procedure ρ 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 A dominated by μ and if the density \(\frac{d\lambda}{d\mu}\) can be closely estimated, then a procedure that is nearly Bayes for μ is also nearly Bayes for λ.
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© 1990 Springer-Verlag New York Inc.
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Le Cam, L., Lo Yang, G. (1990). On Bayes Procedures. In: Asymptotics in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0377-0_7
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DOI: https://doi.org/10.1007/978-1-4684-0377-0_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0379-4
Online ISBN: 978-1-4684-0377-0
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