A partial overview of the theory of statistics with functional data
A partial overview of the theory of statistics with functional data
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DOI：
10.1016/j.jspi.2013.04.002
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发表时间：
2014-04-01
影响因子：
0.9
通讯作者：
Cuevas, Antonio
中科院分区：
文献类型：
--
作者：
Cuevas, Antonio
在可用数据是函数（而不是真实的数字或向量）的情况下，统计方法的理论和实践通常被称为函数数据分析（FDA）。从20世纪90年代末开始，这一主题变得越来越受欢迎，现在是统计学的一个主要研究领域。本文的目的是提供一个简短的教程，以及FDA理论的最新技术水平的部分调查。主题的选择和参考文献清单都远非详尽无遗。为了简洁和可读性，许多有趣的想法和参考资料被省略了。(b)综述了一些特别适合FDA的概率工具。(c)讨论了如何在功能设置中定义和估计通常的中心性参数，均值，中位数和众数。(d)简要介绍FDA中回归、分类、降维和自举方法的主要思想和当前文献。(e)关于FDA软件的一些最终意见。(C)2013爱思唯尔有限公司版权所有。
The theory and practice of statistical methods in situations where the available data are functions (instead of real numbers or vectors) is often referred to as Functional Data Analysis (FDA). This subject has become increasingly popular from the end of the 1990s and is now a major research field in statistics.The aim of this expository paper is to offer a short tutorial as well as a partial survey of the state of the art in FDA theory. Both the selection of topics and the references list are far from exhaustive. Many interesting ideas and references have been left out for the sake of brevity and readability.In summary, this paper provides:(a) A discussion on the nature and treatment of the functional data.(b) A review of some probabilistic tools especially suited for FDA.(c) A discussion about how the usual centrality parameters, mean, median and mode, can be defined and estimated in the functional setting.(d) Short accounts of the main ideas and current literature on regression, classification, dimension reduction and bootstrap methods in FDA.(e) Some final comments regarding software for FDA. (C) 2013 Elsevier B.V. All rights reserved.