1

Im working through the following likelihood ratio problem below (not a homework question, studying for a final).

Given a uniform random sample on $[0, θ]$, derive the likelihood ratio test statistic for parameter θ, for the unconstrained model versus the constrained model $θ ≥ 2$.

I've worked through finding the unconstrained MLE of $X_{(n)}$. How would I proceed with the question? I'm not sure how to represent the constrained model.

kjetil b halvorsen
  • 77,844
bdempe
  • 248
  • 2
  • 8
  • 3
    The actual value of theta will always be greater than the sample maximum. So if X_(n) > 2 you know that any model with theta less than or equal to 2 is wrong. – Michael R. Chernick Dec 08 '16 at 19:58
  • Almost dup: https://stats.stackexchange.com/questions/439034/generalized-likelihood-ratio-in-uniform-distribution, https://stats.stackexchange.com/questions/81225/likelihood-ratio-of-two-sample-uniform-distribution, https://stats.stackexchange.com/questions/515260/critical-region-for-an-uniform-distribution, https://stats.stackexchange.com/questions/521494/applying-wilks-theorem-to-uniform-distribution – kjetil b halvorsen Nov 16 '22 at 18:53

0 Answers0