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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 '13 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 '13 at 22:03
    
Eureka! Actually, the answer was fairly simple. Thank you for the hint. –  babbo natale Jan 14 '13 at 17:19
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can you please write down the answer? thx in advance –  user19742 Jan 16 '13 at 14:47

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