  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.
