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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1996 • Question 7

Question

Math 6010 • Linear Models 1996 • Question 7
Suppose \(X_1,\ldots,X_n\) is an i.i.d. sample from a normal distribution with mean \(\mu\) and variance 1. **(a)** Find the UMVU estimator for \(\mu\). (Prove the optimality criterion.) **(b)** Put a \(N(\theta,\tau^2)\) prior on \(\mu\) and find the minimax estimator of \(\mu\).

Raw LaTeX

Suppose \(X_1,\ldots,X_n\) is an i.i.d. sample from a normal distribution with mean \(\mu\) and variance 1.
\begin{parts}
\item Find the UMVU estimator for \(\mu\). (Prove the optimality criterion.)
\item Put a \(N(\theta,\tau^2)\) prior on \(\mu\) and find the minimax estimator of \(\mu\).
\end{parts}

Topic Tags

Bayesian Testing and Decision Theory Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods