On the admissibility of estimators of the zero class in poisson populations

Abstract

Let T = x₁+ x₂ + … + x_n where x₁,…, x_n are independent and identically distributed randon variables each having a poission distribution with mean θ. It is proved that each of the estimators ((n+k−1)/(n+k))^T, k = 0,1,2,… is admissible for estimating exp(−θ) when the loss function is squared error.

Keywords:

• admissible estimator
• Bayes estimator
• Bayes risk
• improper prior
• loss function
• Poisson