Nonparametric analysis of multivariate data

多元数据的非参数分析

• 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

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.

我们正处于大规模自动数据收集的时代。观察常常具有数千或数十亿的维度。经典的方法不是为了科普这种增长的观察维度。我的研究建议涉及开发新的方法和改进现有的非参数数据分析方法的情况下，一个单一的观察是高维的。 我对多元非参数模型中的估计和检验问题感兴趣。在这样的模型中，人们经常观察到一个函数，或信号，（无限）许多变量与弱噪声混合。根据可用的观察结果，问题是从有噪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。经典的统计估计和检验理论通常对用来描述现实生活中现象的统计模型有很大的限制。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较强的普适性，在实际中得到了广泛的应用。 我还计划研究一些与发现非参数检验程序的效率相关的问题。计算非参数检验的效率是一个重要的问题。效率的知识为我们提供了一个指导线索，在现有的测试程序的多样性方向，并允许我们选择最好的测试。 作为一个整体，该项目预计将有助于开发新的工具，用于今天的多元数据分析。