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

By

CUN-HUI ZHANG 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.

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