Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2017 • Question 3

Question

Math 6010 • Linear Models Fall 2017 • Question 3

Let \(X_1,X_2,\ldots ,X_n\) be iid random variables with density \[ h(t;\theta )=\theta t^{\theta -1}I\{0\leq t\leq 1\}, \qquad \theta >0. \] Find the maximum likelihood estimator of \(\theta \) and compute the asymptotic variance of the maximum likelihood estimator.

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be iid random variables with density
\[
  h(t;\theta)=\theta t^{\theta-1}I\{0\leq t\leq 1\}, \qquad \theta>0.
\]
Find the maximum likelihood estimator of \(\theta\) and compute the asymptotic
variance of the maximum likelihood estimator.

Topic Tags

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