Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2008 • Question 1

Question

Math 6010 • Linear Models Spring 2008 • Question 1

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

1a) (5 points) Find the MLE \(\hat \eta \) and compute its pdf. Do you recognize it?

1b) (5 points) Is \(\hat \eta \) unbiased, asymptotically unbiased, MSE consistent, simple consistent?

Raw LaTeX

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

\textbf{1a)} (5 points) Find the MLE \(\hat\eta\) and compute its pdf. Do you
recognize it?

\textbf{1b)} (5 points) Is \(\hat\eta\) unbiased, asymptotically unbiased, MSE
consistent, simple consistent?

Topic Tags

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