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.

翻译：考虑一个已知一个部件密度的双级混合物模型。我们讨论了对第二个部件未知概率密度的非参数适应性估计问题。我们提议了一个随机加权内核测深器,并本着Goldenshluger和Lepski方法的精神,采用完全以数据驱动的带宽选择方法。对点偏差风险的甲骨文型不平等以及控者平滑等级的趋同率都得到了推导。理论结果通过数字模拟来说明。