UNBIASED ESTIMATORS OF A LATTICE MIXING DISTRIBUTION AND THE CHARACTERISTIC FUNCTION OF A GENERAL MIXING DISTRIBUTION
Cun‐Hui Zhang · 1999
SUMMARY. Let f(x|θ) be a known parametric family of probability density functions with respect to a σ-finite measure µ. The density function f(x) of a random variable X belongs to a mixture model if f(x) = � f(x|θ)dG(θ). We derive unbiased estimators of the characteristic functions of the mixing distribution G under some integrability conditions on G and the probability mass function of G when G is a lattice distribution. Upper bounds for the variances of these unbiased estimators are provided. Three types of exponential families and a location-type model are considered, including the Poisson and gamma families. 1.