Nonparametric analysis of multivariate data

多元数据的非参数分析

基本信息

批准号：
293280-2010
负责人：
Stepanova, Natalia
金额：
$ 1.46万
依托单位：
Carleton University
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2015
资助国家：
加拿大
起止时间：
2015-01-01 至 2016-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571427
关键词：
Nonparametric analysis multivariate data

项目摘要

We are in the era of massive automatic data collection. Often observations have dimensions of thousands or billions. Classical methods are not designed to cope with this kind of growth of observations dimensionality. My research proposal involves developing new methods and improving the existing nonparametric methods of data analysis in the case when a single observation is of high dimension. I am interested in estimation and testing problems in multivariate nonparametric models. In such models one often observes a function, or signal, of (infinitely-) many variables mixed with a weak noise. Based on the observations available, the problems are to recover the signal from noisy data and to find out whether or not the signal does exist. The first problem is called an estimation problem, the second one is known as a signal detection problem. The classical theory of statistical estimation and testing usually puts heavy restrictions on the statistical models that are used to describe the real-life phenomena. Modern nonparametric statistics makes noticeably fewer assumptions about the models. As a result, the methods of modern nonparametric statistics are rather universal and widely applied in practice. I also plan to work on some problems related to finding efficiency of nonparametric test procedures. The problem of calculating efficiency of nonparametric tests is important. The knowledge of efficiency give us a guiding thread for orientation in the diversity of existing test procedures and allows us to choose the best test available. As a whole, the project is expected to contribute towards developing new tools to be used in multivariate data analysis today.

我们正处于海量自动数据收集的时代。通常观察的维度有数千或数十亿。经典方法并不是为了应对这种观测维度的增长而设计的。我的研究建议涉及在单个观测值具有高维度的情况下开发新方法并改进现有的非参数数据分析方法。我对多元非参数模型中的估计和测试问题感兴趣。在此类模型中，人们经常观察到由（无限）多个变量与微弱噪声混合而成的函数或信号。根据现有的观察结果，问题是从噪声数据中恢复信号并查明信号是否确实存在。第一个问题称为估计问题，第二个问题称为信号检测问题。统计估计和检验的经典理论通常对用于描述现实生活现象的统计模型施加严格限制。现代非参数统计对模型的假设明显减少。因此，现代非参数统计方法具有相当的普适性，在实践中得到广泛应用。我还计划研究一些与寻找非参数测试程序的效率相关的问题。非参数检验的计算效率问题很重要。效率知识为我们提供了指导现有测试程序多样性的指导方针，并使我们能够选择可用的最佳测试。总体而言，该项目预计将有助于开发当今多变量数据分析中使用的新工具。