Lecture 15. B) Some Implications

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Some Implications

  • If one has access to [math]I\left(\theta_{0}\right)^{-1}[/math], or one can approximate it via some estimator say [math]\widehat{I\left(\theta_{0}\right)}[/math] and/or [math]\widehat{I\left(\theta_{ML}\right)}[/math], one can use the normal distribution for hypothesis testing as long as [math]n[/math] is large.
  • The point above applies, even if one does not know the exact distribution of the test.
  • It can be shown that the LRT, Wald, and LM tests are asymptotically equivalent. The proof, perhaps unsurprisingly, uses Taylor expansion.