Let c > 0 and consider the loss function Assume that has a continuous distribution. Prove

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Let c > 0 and consider the loss function

Assume that Î¸ has a continuous distribution. Prove that a Bayes estimator of Î¸ will be any 1/(1+ c) quantile of the posterior distribution of Î¸. The proof is a lot like the proof of Theorem 4.5.3. The result holds even if Î¸ does not have a continuous distribution, but the proof is more cumbersome.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

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Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

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Question Posted: Nov 25, 2015 03:57 AM

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Let c > 0 and consider the loss function Assume that has a continuous distribution. Prove

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| cle – al if e < a, if ez a. 18 - al if 0z a. L(0, a) = 1e - al

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Let a 0 be a 11 c quantile of the posterior distribution and let a1 be some other value Assume that ...View the full answer

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