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 Poisson distribution with parameter θ, 0 < θ < ∞. Let Y =Σn1 Xi and let L[θ, δ(y)] = [θ − δ(y)]2. If we restrict our considerations to decision functions of the form δ(y) = b + y/n, where b does not depend on y, show that R(θ, δ) = b2+θ/n. What decision function of this form yields a uniformly smaller risk than every other decision function of this form? With this solution, say δ, and 0 < θ < ∞, determine maxθ R(θ, δ) if it exists.
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a Let yi denote the value of Y at the end of the nth trial Then yi n1 Xi and so y yn yn 1 B...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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