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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2008 • Question 2

Question

Math 6010 • Linear Models Spring 2008 • Question 2

Let \(X_i\) be a random sample of size \(n\) with pdf \(f(x;\theta )=\frac {1}{\theta }e^{-(x-\theta )/\theta }\) (\(x>\theta \), \(\theta >0\)).

2a) (5 points) What is the MME of \(\theta \)? Is it a reasonable estimator?

2b) (5 points) What is the MLE of \(\theta \)?

Raw LaTeX

Let \(X_i\) be a random sample of size \(n\) with pdf
\(f(x;\theta)=\frac{1}{\theta}e^{-(x-\theta)/\theta}\) (\(x>\theta\),
\(\theta>0\)).

\textbf{2a)} (5 points) What is the MME of \(\theta\)? Is it a reasonable
estimator?

\textbf{2b)} (5 points) What is the MLE of \(\theta\)?

Topic Tags

Estimator Distributions Maximum Likelihood Estimation Measure-Theoretic Probability Uniform Integrability and Truncation Methods