Statistical inference on the shape of multivariate curves: mode detection, level set estimation and classification

该项目的目的是开发灵活的非参数程序来对多变量曲线的形状进行推断。对于多变量曲线，出现了一些新的问题，这些问题在研究得更充分的一维情况下是不存在的。我们提出了在模式检测、水平集估计和分类方面要做的研究。模式的数量和位置给人对曲线形状的第一印象。对模式的估计通常基于对观测集中的区域的搜索。这与密度水平集的估计有关。另一方面，当设计分类程序时，人们必须找到最优决策集。寻找最优决策集的技术通常与水平集估计技术密切相关。研究建议包括在统计程序的数学分析以及快速算法和图形工具的设计方面要做的工作。除了发布结果外，我们还打算实施算法和分发软件。

The purpose of the project is to develop flexible nonparametric procedures for making inference on the shape of multivariate curves. For multivariate curves several new problems arise, which are not present in the more well studied one dimensional case. We propose research to be done on mode detection, level set estimation and classification. Number and location of modes give a first impression on the shape of a curve. Estimation of modes is typically based on searches of regions where observations are concentrated. This is connected to the estimation of level sets of densities. On the other hand, when designing classification procedures one has to find optimal decision sets. Techniques to find optimal decision sets are often closely related to techniques for the estimation of level sets. The research proposal includes work to be done both in mathematical analysis of statistical procedures and also designing of fast algorithms and graphical tools. We intend to implement algorithms and distribute software in addition to the publication of the results.