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.
Asked
Active
Viewed 106 times
1
kjetil b halvorsen
- 63,378
- 26
- 142
- 467
Shorty12319
- 21
- 2
-
2Most functions of $\theta$ do not enjoy the existence of an unbiased estimator. – Xi'an Nov 24 '20 at 16:43
-
2Use the methods illustrated by the similar question at https://stats.stackexchange.com/questions/87107. – whuber Nov 24 '20 at 17:08
-
It would imply $\varphi(0)=+\infty$... – Xi'an Nov 24 '20 at 17:20