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Counterexamples
› Estimation
Is this true?
The MLE is unique
No — it is false.
statistics
Others that fail the same way
A sufficient statistic is complete
The Cramér–Rao bound is attained by the UMVUE
The MLE is unbiased
A UMP test exists for every testing problem
Any interval of the form [X̄ − (S/√n)t, ∞) with a 90% quantile t is a 90% confidence interval
OLS is the BLUE in every linear model
From
Estimation › MLE and method of moments
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