Find the maximum likelihood estimator(MLE) of $X_1,X_2,...,X_n\sim$ Unif $(-a,a)$.
I've tried using the likelihood function but end up getting $0$. I then tried $\max(|Xi|)$ but not sure if this is considered a maximum likelihood estimator.
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zaira
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user538173
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The likelihood function is $$L(a;X_1,X_2,\ldots,X_n) = \begin{cases}(2a)^{-n}, & \text{if } \max(|X_i| : 1 \leq i \leq n) \leq a \ 0, & \text{otherwise}\end{cases}$$ Its maximum doesn't occur at $a=0$ because this will undoubtedly be in the second "otherwise" case, giving $0$. – Brian Moehring Oct 01 '20 at 03:41
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6Does this answer your question? Maximum Likelihood Estimator for $\theta$ when $X_1,\dots, X_n \sim U(-\theta,\theta)$ – zaira Oct 01 '20 at 05:27