On UMVU estimators and Bhattacharya bounds in exponential distributions (Q794362)

A subfamily of exponential distributions with densities \(f(x,\theta)= \exp [t(x)\psi_ 1(\theta)-\psi_ 2(\theta)]\) is considered. It is proved that for estimable functions g of \(\theta\) the variance of the UMVU (Uniformly Minimum Variance Unbiased) estimator is the limit of Bhattacharya bounds if g possesses a power series expansion. The Poisson, normal and exponential distributions are studied as examples.