论文标题
两级混合模型中组件密度的自适应非参数估计
Adaptive nonparametric estimation of a component density in a two-class mixture model
论文作者
论文摘要
考虑了一个两类混合模型，其中已知其中一个组件的密度。我们解决了第二个成分未知概率密度的非参数自适应估计的问题。我们以Goldenshluger和Lepski方法的精神提出了一个随机加权的内核估计器。对于次数二次风险的Oracle型不平等，以及持有器平滑度类别的收敛率。理论结果通过数值模拟说明。
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Holder smoothness classes. The theoretical results are illustrated by numerical simulations.
