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.

翻译：非参数最大可能性估计旨在推断未知密度分布,同时尽可能少地作出假设。为了减轻非参数数据匹配中的超参数化,平滑的假设通常会并入估算。本文对单体情况下的非参数估计采用了一种新的推进法。我们用非参数对日志相似性第二阶近似值推算推算推算法。高斯内核和光滑的样条被选为弱学习者,在推进时满足平滑的假设。模拟和真实数据实验显示了拟议方法的功效。