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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 10

Question

Math 6010 • Linear Models Spring 2015 • Question 10

Let \(X_1,\ldots ,X_n\) be a random sample from \(\operatorname {Uniform}[0,\theta ]\), where \(\theta \) is a positive unknown. Derive the generalized likelihood ratio (GLR) test of \(H_0:\theta =\theta _0\) vs. \(H_a:\theta \ne \theta _0\).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample from \(\UNIF[0,\theta]\),
where \(\theta\) is a positive unknown. Derive the generalized likelihood ratio
(GLR) test of \(H_0:\theta=\theta_0\) vs. \(H_a:\theta\ne\theta_0\).

Topic Tags

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