Sankhya: The Indian Journal of Statistics
1999, Volume 61, Series A, Pt. 1 ,pp. 101--112
UNBIASED ESTIMATORS OF A LATTICE MIXING DISTRIBUTION AND THE CHARACTERISTIC FUNCTION OF A GENERAL MIXING DISTRIBUTION
Rutgers University, Piscataway
SUMMARY. Let f(x|q) be a known parametric family of probability density functions with respect to a s-finite measure m. The density function f(x) of a random variable X belongs to a mixture model if f(x)=\int f(x|\theta)dG(\theta)$. 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.
AMS (1991) subject classification.Primary 62G05; secondary 62G20.
Key words and phrases. Mixture, mixing distribution, unbiasedness, Fourier transformation.
Full paper (PDF)
This article in Mathematical Reviews