Estimation and beyond in the Bayes Universe. 1.1 Estimation
نویسنده
چکیده
This implies that the Bayes risk is 0. The Bayes risk of δπ(X) can be calculated as repeated expectation in two ways, r(π, δπ) = EθEX|θ(θ − δπ(X)) = EXEθ|X(θ − δπ(X)). Thus, conveniently choosing either EθEX|θ or EXEθ|X and using the properties of conditional expectation we have, r(π, δπ) = EθEX|θθ2 −EθEX|θθδπ(X)−EXEθ|Xθδπ(X) + EXEθ|Xδ2 π(X) = EθEX|θθ2 −Eθθ[EX|θδπ(X)]− EXδπ(X)Eθ|Xθ + EXEθ|Xδ2 π(X) = EθEX|θθ2 −Eθθ · θ − Eδπ(X)δπ(X) + EXEθ|Xδ2 π(X) = 0.
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تاریخ انتشار 2004