Question

Instructions: For each of the following distributions, compute the maximum likelihood estimator based on n i.d. observations X····, Xn and the Fisher information, if defined. If it is not, enter DNE in each applicable input box. which means that each X1 has density exp (-( 1)2 202 Hint: Keep in mind that we consider σ2 as the parameter, not σ . You may want to write τ-σ2 in your computation. (Enter barx_n for the sample average Xn and bar(X_n 2) for the sample average of second moments X Maximum likelihood estimator μ = (Enter barx_n for the sample average Xn and bar(X nA2) for the sample average of second moments X?) Maximum likelihood estimator σ2 Hint: One of the formulas for Fisher information will lead to a much shorter computation. (f the Fisher information is not defined, enter DNE for all boxes below.) 1,1 2,1 Using the Fisher Information you obtain above, what is the asymptotic variance V (σ*) of the MLE σ2 ?Compare this with your result from Homework 5 Problem 3.

Answer 1

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