In this section, it was established that and X are both sufficient statistics for estimating the parameter of a Poisson distribution We know that E(X) , but it is also true that E(S 2 ) 2 for Poisson data So, another unbiased estimator for is Which of these three estimators X, S 2 , or is the best ...

In the context of estimating the parameter of a Poisson distribution the best choice among the three ...

In this section, it was established that and X are both sufficient statistics for estimating the parameter

Question:

In this section, it was established that and X̅ are both sufficient statistics for estimating the parameter μ of a Poisson distribution. We know that E(X̅) = μ, but it is also true that E(S²) = σ²= μ for Poisson data. So, another unbiased estimator for μ is Which of these three estimators— X̅, S², or is the best choice for estimating μ? Why?