论文标题
大型功能数据的统计深度，并应用于神经影像学
Statistical Depth for Big Functional Data with Application to Neuroimaging
论文作者
论文摘要
功能深度是订购功能数据集的功能数据分析技术。与真实行上的数据情况不同，定义此顺序是不平凡的，尤其是在功能数据的情况下，任何深度都应满足的属性。我们提出了一个新的深度，这两者都满足功能深度所需的属性，也可以在有大量功能观测值或观察值是几个连续变量（例如图像）函数的情况下使用的情况。我们为我们选择提供理论上的理由，并通过模拟评估我们提出的深度。最终，我们将提出的深度应用于产生正电子发射断层扫描（PET）数据完全非参数解卷积的问题，以在整个图像中大量曲线，以及从一组PET扫描中找到代表性受试者的问题。
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of properties that any depth should satisfy. We propose a new depth which both satisfies the properties required of a functional depth but also one which can be used in the case where there are a very large number of functional observations or in the case where the observations are functions of several continuous variables (such as images, for example). We give theoretical justification for our choice, and evaluate our proposed depth through simulation. We finally apply the proposed depth to the problem of yielding a completely non-parametric deconvolution of Positron Emission Tomography (PET) data for a very large number of curves across the image, as well as to the problem of finding a representative subject from a set of PET scans.
