A continuous estimator of a distribution function that reproduces the empirical moments

Abstract

Suppose we have a random sample from a continuous distribution function with support on the positive reals. This paper will investigate a semi-parametric estimator of the distribution function that is based on mixtures of lognormal distributions. This estimator will be constructed so that a specified number of moments of the empirical distribution function are reproduced. We will give several asymptotic results for this moment-type estimator including a central limit theorem.

Keywords:

• semi-parametric estimator
• empirical moments empirical distribution function
• mixtures of lognormal distributions
• asymptotic consistency