Question

Concept Question: Maximum Likelihood Estimator for the Laplace distribution 1 point possible (graded) As in the previous problem, let mn MLE denote the MLE for an unknown parameter m* of a Laplace distribution. MLE Can we apply the theorem for the asymptotic normality of the MLE to mn? (You must choose the correct answer that also has the correct explanation.) No, because the log-likelihood is not concave. No, because the log-likelihood is not twice-differentiable, so the Fisher information does not exist. Yes, because the log-likelihood is concave. Yes, because the other technical conditions required to apply the theorem are satisfied. Submit You have used 0 of 2 attempts Save

Answer 1

The 4th option is correct.

Under certain regularity conditions, mle of a parameter in any distribution setup, has an asymptotic normal distribution. This holds for any distribution for which the regularity holds good. It can be shown that for laplaLa distribution, these regularity conditions hold true.(proof of this is out of the scope of this question) Hence the mle is asymptotically normal.

Other options are incorrect for obvious reasons.

Hope the solution helps. Thank you.

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