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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2017 • Question 2

Question

Math 6010 • Linear Models Fall 2017 • Question 2

Let \(X_1,X_2,\ldots ,X_n\) be iid random variables with density function \[ h(t;\eta )=e^{-(t-\eta )}I\{t\geq \eta \}, \] where \(I\) indicates the indicator function. We want to test \(H_0:\eta =\eta _0\) against \(H_A:\eta \ne \eta _0\). Find a test using the likelihood method and compute the power function.

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be iid random variables with density
function
\[
  h(t;\eta)=e^{-(t-\eta)}I\{t\geq\eta\},
\]
where \(I\) indicates the indicator function. We want to test \(H_0:\eta=\eta_0\)
against \(H_A:\eta\ne\eta_0\). Find a test using the likelihood method and
compute the power function.

Topic Tags

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