标题： 密度模型中过量质量估计的函数方法 显示英文标题

标题： Functional approach for excess mass estimation in the density model

摘要： 我们考虑一个多元密度模型，在该模型中，我们从 $n$ 个独立同分布的观测随机变量估计未知概率密度 $f$ 在给定水平 $\nu>0$ 下的超额质量。 这个问题有多种应用，例如多模态检验、密度轮廓聚类、异常检测、分类等。 文献中首次我们将超额质量估计为未知密度 $f$ 的积分泛函。我们提出了一种估计器，并评估了其收敛速度，当 $f$ 属于一般 Besov 光滑性类时，针对多种风险度量进行了讨论。 特别注意了所研究方法的实现和数值研究。 结果表明，我们的方法改进了超额质量的嵌入式估计器。 显示英文摘要

摘要： We consider a multivariate density model where we estimate the excess mass of the unknown probability density $f$ at a given level $\nu>0$ from $n$ i.i.d. observed random variables. This problem has several applications such as multimodality testing, density contour clustering, anomaly detection, classification and so on. For the first time in the literature we estimate the excess mass as an integrated functional of the unknown density $f$. We suggest an estimator and evaluate its rate of convergence, when $f$ belongs to general Besov smoothness classes, for several risk measures. A particular care is devoted to implementation and numerical study of the studied procedure. It appears that our procedure improves the plug-in estimator of the excess mass.