Optimal convergence rates for good's nonparametric maximum likelihood density estimator

摘要

We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to L~1 convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the rough-ness penalized estimator.