Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 8

Question

Math 6010 • Linear Models Spring 2016 • Question 8

Let \(Y_1<Y_2<\cdots <Y_5\) be the order statistics of a random sample of size \(n=5\) from a distribution with pdf \(f(x;\theta )=e^{-|x-\theta |}/2\), \(-\infty <x<\infty \), with \(\theta \) unknown. Find the likelihood ratio test \(\lambda \) for testing \(H_0:\theta =\theta _0\) versus \(H_1:\theta \ne \theta _0\).

Raw LaTeX

Let \(Y_1<Y_2<\cdots<Y_5\) be the order statistics of a random sample
of size \(n=5\) from a distribution with pdf
\(f(x;\theta)=e^{-|x-\theta|}/2\), \(-\infty<x<\infty\), with \(\theta\) unknown.
Find the likelihood ratio test \(\lambda\) for testing \(H_0:\theta=\theta_0\)
versus \(H_1:\theta\ne\theta_0\).

Topic Tags

F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation Uniform Integrability and Truncation Methods