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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2016 • Question 9

Question

Math 6010 • Linear Models Fall 2016 • Question 9

Let \(X_1,X_2,\ldots ,X_n\) be a random sample from a Gamma\((\alpha ,\theta )\) distribution, with \(\alpha \) known and \(\theta \) unknown. Find the Fisher information of this distribution and show that the MLE of \(\theta \) is an efficient estimator of \(\theta \).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be a random sample from a
Gamma\((\alpha,\theta)\) distribution, with \(\alpha\) known and \(\theta\) unknown.
Find the Fisher information of this distribution and show that the MLE of
\(\theta\) is an efficient estimator of \(\theta\).

Topic Tags

Estimator Distributions Maximum Likelihood Estimation Multivariate Normal Distributions Uniform Integrability and Truncation Methods