Consistency of Two Nonparametric Maximum Penalized Likelihood Estimators of the Probability Density Function

摘要

This reprint studies the consistency properties of a nonparametric estimator of a density function on the real line, which is known as the first MPLE of Good and Gaskins, and which is obtained by maximizing the likelihood functional multiplied by a roughness penalty with alpha > 0. Keywords; Convergence; and Consistency.