Estimation of poisson means under weighted squared error loss

In estimating the means of several independent Poisson distributions, we show that the maximum likelihood estimator is inadmissible when general weighted squared error loss is the criterion. Using this result, we extend the known results on estimation of several Poisson means (Peng 1975, Hudson 1978) to the case where possibly more than one observation is taken from each Poisson distribution and the samples are not necessarily of the same size.