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Let X_1,..., X_n be a random sample from a n(theta, sigma^2) population, sigma ^

ID: 3377352 • Letter: L

Question

Let X_1,..., X_n be a random sample from a n(theta, sigma^2) population, sigma ^2 known. Consider estimating theta using squared error loss. Let pi(theta) be a n(mu, tau ^2) prior distribution on theta and let delta ^pi be the Bayes estimator of theta. Verify the following formulas for the risk function and Bayes risk. For any constants a and b, the estimator delta(x) = aX- + b has risk function Let eta = sigma^2/(n tau^2 + sigma ^2). The risk function for the Bayes estimator is The Bayes risk for the Bayes estimator is B(pi, delta ^pi) = r^2 eta.

Explanation / Answer

Let X_1,..., X_n be a random sample from a n(theta, sigma^2) population, sigma ^

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