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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2008 • Question 3

Question

Math 6010 • Linear Models Spring 2008 • Question 3

(10 points) Let \(X_i\sim \operatorname {POI}(\mu )\) be a random sample of size \(n\). Find the MLE of \(e^{-\mu }\). Is it unbiased, asymptotically unbiased, MSE consistent, simple consistent? [Hint: The MGF of \(\operatorname {POI}(\mu )\) is \(e^{\mu (e^t-1)}\).]

Raw LaTeX

(10 points) Let \(X_i\sim\operatorname{POI}(\mu)\) be a random sample
of size \(n\). Find the MLE of \(e^{-\mu}\). Is it unbiased, asymptotically
unbiased, MSE consistent, simple consistent? [Hint: The MGF of
\(\operatorname{POI}(\mu)\) is \(e^{\mu(e^t-1)}\).]

Topic Tags

Maximum Likelihood Estimation Uniform Integrability and Truncation Methods