Comparison of two estimators

120 Views Asked by At

Let $X$ be distributed as a Poisson($\lambda$) such that it's density is given by

$$\mathbb{P}_\lambda(X=x) =\frac{\lambda^x e^{-\lambda}}{x!}$$

Compare the following estimators of $g(\lambda)=e^{-\lambda}$,

$$ \begin{align} T1 &= e^{-\bar X}\\ T2 &= \frac{\sum_{i=1}^nI(Xi=0)}{n} \end{align} $$

I am studying consistency bias and stuff like that, but I do know how to set up this exercise to compare these 2 estimators Can someone just give an hint ? it would be very appreciate