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 letter 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.

中文翻译：

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单变量非参数最大似然估计的提升

非参数最大似然估计旨在推断未知的密度分布，同时做出尽可能少的假设。为了减轻非参数数据拟合中的过度参数化，通常将平滑假设合并到估计中。在这封信中，将一种新颖的基于提升的方法引入到单变量情况下的非参数估计中。我们通过非参数对数似然的二阶近似来推导升压算法。选择高斯核和平滑样条作为满足平滑假设的弱学习者。仿真和真实数据实验证明了该方法的有效性。