Statistics Graduate Level Quiz
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ASYMPTOTIC THEORY
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Let X1,…,XnX_1,\ldots,X_n be independent with density f(x;θ)=θ−11{0<x<θ}f(x;\theta)=\theta^{-1}\mathbf{1}\{0<x<\theta\}, where the true parameter is θ0>0\theta_0>0. The maximum likelihood estimator is θ^n=max⁡iXi\widehat\theta_n=\max_i X_i.
Which statement best describes the asymptotic behavior of the MLE and the regularity issue responsible for it?
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