Boosting in Univariate Nonparametric Maximum Likelihood Estimation

TL;DR

This paper introduces a boosting-based method for univariate nonparametric maximum likelihood estimation, combining smoothing techniques with boosting to improve density inference with minimal assumptions.

Contribution

It proposes a novel boosting algorithm derived from second-order approximation of the nonparametric log-likelihood, integrating Gaussian kernels and splines as weak learners.

Findings

Effective in simulations and real data experiments

Reduces overparameterization in nonparametric density estimation

Demonstrates improved estimation accuracy

Abstract

Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are usually merged into the estimation. In this paper a novel boosting-based method is introduced to the nonparametric estimation in univariate cases. We deduce the boosting algorithm by the second-order approximation of nonparametric log-likelihood. Gaussian kernel and smooth spline are chosen as weak learners in boosting to satisfy the smoothing assumptions. Simulations and real data experiments demonstrate the efficacy of the proposed approach.