Let X 1 ,X 2 , . . . , X n denote a random sample from
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Let X1,X2, . . . , Xn denote a random sample from a distribution that is N(μ, θ), 0 < θ < ∞, where μ is unknown. Let Y = Σn1 (Xi − ‾X)2/n and let L[θ, δ(y)] = [θ−δ(y)]2. If we consider decision functions of the form δ(y) = by, where b does not depend upon y, show that R(θ, δ) = (θ2/n2) [(n2−1)b2−2n(n−1)b+n2]. Show that b = n/(n+1) yields a minimum risk decision function of this form.
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a We have Y n1 X1 Xi X2n so a decision rule y b by is e...View the full answer
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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