Limit distributions of unbiased estimators in natural exponential families
Fernando López-Blázquez, Begoña Salamanca-Miño · Statistics · 2002
We obtain the possible limit distributions of unbiased estimators of functions of the parameter of a natural exponential family. The limit distribution depends on j, the order of the first non-zero derivative at the true (but usually unknown) value of the parameter. We show that if j \geq 2 then the umvu and the maximum likelihood estimators are not asymptotically equivalent.