The decision theoretic approach to set estimation can be quite useful (see Exercise 9.56) but it can
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L((μ, Ï), C) = b Length(C) - IC(μ),
similar to that used in Exercise 9.54, but without scaling the length. Construct another procedure C' as
where K is a positive constant. C' does exactly the wrong thing. When s2 is big and there is a lot of uncertainty, we would want the interval to be wide. But C' is empty! Show that we can find a value of K so that
R((μ, Ï),C') ¤ R(μ, Ï),C) for every (μ, Ï)
with strict inequality for some (μ, Ï).
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