On Limiting Distributions of UMVUE of Central Moments
Narges Abbasi · 2008
In the theory of U-statistics, we consider a functional θ defined on a set F of distribution functions on R: θ = θ(F) , F ∈ F. The θ∈θ(F) estimated by using a sample from the random variables X1, X2,..., Xn, which are independently and identically distributed with distribution function F. Halmos [1] proved that the functional θ admits an unbiased estimator if and only if there is a function h of k variables such that