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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 3

Question

Math 6010 • Linear Models Spring 2009 • Question 3

Let \(X_1,\ldots ,X_n\) be a random sample from \(N(\theta ,\theta )\), where \(\theta >0\). In particular, the population mean and the population variance are equal but unknown.

(a) Find the method-of-moments estimator of \(\theta \) based on the second sample moment.

(b) Find the maximum likelihood estimator of \(\theta \).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample from \(\N(\theta,\theta)\),
where \(\theta>0\). In particular, the population mean and the population variance
are equal but unknown.

\textbf{(a)} Find the method-of-moments estimator of \(\theta\) based on the
second sample moment.

\textbf{(b)} Find the maximum likelihood estimator of \(\theta\).

Topic Tags

Analysis of Variance Estimator Distributions Maximum Likelihood Estimation Uniform Integrability and Truncation Methods