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MLE and sufficient statistic


Jan 17, 2013
Hi! I was wondering

In my note we've a Corollary saying:

If T is sufficient for \(\displaystyle \Theta\), the maximum likelihood estimate is a function of T.

where T is \(\displaystyle T(X_1,X_2,...X_n) \)and X is given by\(\displaystyle f(x|\Theta)\)

I was wondering, isn't every Maximum likelihood estimator a sufficient statistic?

Thanks for passing by!
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