标题： 函数设置下的DD$^G$-分类器 显示英文标题

标题： The DD$^G$-classifier in the functional setting

摘要： 最大深度（Maximum Depth）是首次尝试使用数据深度而非多变量原始数据来构建分类规则。近期，DD-分类器解决了最大深度分类器的几个严重局限性，但仍存在一些问题。本文致力于以以下方式扩展DD-分类器：首先，克服当涉及两个以上组别时DD-分类器的局限性；其次，将常规分类方法（如$k$NN、线性或二次分类器、递归分割等）应用于DD图，通过这些方法的诊断获得有用的见解；第三，在分类过程中以统一的方式整合不同来源的信息（数据深度或多变量函数数据）。此外，由于DD-分类器技巧在函数框架中特别有用，本文还对几种函数数据深度进行了增强修订。同时，提供了模拟研究和对一些经典真实数据集的应用，展示了新建议的强大功能。 显示英文摘要

摘要： The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some issues still remain. This paper is devoted to extending the DD-classifier in the following ways: first, to surpass the limitation of the DD-classifier when more than two groups are involved. Second to apply regular classification methods (like $k$NN, linear or quadratic classifiers, recursive partitioning,...) to DD-plots to obtain useful insights through the diagnostics of these methods. And third, to integrate different sources of information (data depths or multivariate functional data) in a unified way in the classification procedure. Besides, as the DD-classifier trick is especially useful in the functional framework, an enhanced revision of several functional data depths is done in the paper. A simulation study and applications to some classical real datasets are also provided showing the power of the new proposal.