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Inferential Statisticshard
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Consider a non-regular case for MLE where the density f(x∣θ)=1f(x|\theta) = 1f(x∣θ)=1 for θ−1/2<x<θ+1/2\theta - 1/2 < x < \theta + 1/2θ−1/2<x<θ+1/2. What is the asymptotic behavior of the MLE θ^n\hat{\theta}_nθ^n​?