Nonparametric Estimators of a Distribution Funtion Based on Mixtures of Gamma Distributions

Suppose we have a random sample from a continuous distribution function with support on the positive reals. This paper will investigate nonparametric estimators of the distribution function that are based on mixtures of gamma distributions. First we give several asymptotic results for a kernel-type estimator including order results and a central limit theorem. Next, we consider a moment-type estimator that is constructed by using empirical moment matrices. This estimator will have the property that many of its' moments are equal to the moments of the empirical distribution function.