# Function of an efficient estimator

Let T be an efficient estimator for a parameter $\theta$. Let $g(\cdot)$ be a (real valued) non-linear function. Is $g(T)$ an UMVUE for $g(\theta)$?

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Is this homework? If so, please use the homework tag. – jbowman Jan 11 at 20:52
What is your definition of efficient here? In any event, hint: let $g$ be an arbitrary strictly convex function. – cardinal Jan 12 at 22:03
Eureka! Actually, the answer was fairly simple. Thank you for the hint. – babbo natale Jan 14 at 17:19