Let $X_1, . . . , X_n$ be a sample from the Poisson distribution with the parameter $\theta$. How to prove that there are no unbiased estimators for $\theta^{−2}$? I have no idea that why there are no at all.
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kjetil b halvorsen
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2Most functions of $\theta$ do not enjoy the existence of an unbiased estimator. – Xi'an Nov 24 '20 at 16:43
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2Use the methods illustrated by the similar question at https://stats.stackexchange.com/questions/87107. – whuber Nov 24 '20 at 17:08
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It would imply $\varphi(0)=+\infty$... – Xi'an Nov 24 '20 at 17:20