Multivariate Nonparametric Methodology Studies

多元非参数方法研究

• 批准号: 0907491
• 负责人: David Scott
• 金额: $ 10万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907491&HistoricalAwards=false
• 关键词: Multivariate; Nonparametric; Methodology; Studies

The demands on statistical methodology have grown relentlessly as new technologies for data collection appear. Many of the resulting datasets are unusual by statistical standards: massive and highly nonlinear with contamination. Sometimes the data come from a mechanism which is only partially known. The tasks of estimation, testing, functional testing, pattern discovery, feature extraction, visualization, and comparison require the statistician look at each problem anew. Nonparametric methodology, which has been widely used in one and two dimensions, is also appropriate in these higher dimensions. Particular emphasis will be given to multivariate regression and density estimation problems, and closely related applications such as clustering, mixture estimation, pattern recognition, robust estimation, and dimension reduction. The statistician's view of the scientific method is as a continuously improving process of model building, data collection, estimation, criticism, and refinement. However, many practicing statisticians are stymied by an inability to repair poorly fitting models. Of particular interest in this research are methods which provide critical diagnostic information as part of the model estimation task. A focus of this research is a particular minimum-distance data-based parametric estimation algorithm, which has been investigated for its robustness properties. The algorithm can be applied to mixture models and spline fitting. An incomplete density model may be fitted, a unique capability that will be explored fully in the context of regression, image processing, clustering, outlier detection, and density estimation. Nonparametric methodology for functional data analysis will be devised and tested with novel data sources.Other applications include adaptive wavelet thresholding, solution of the mixture of regression problems, and application to models which apply to only a subset of the data.Research in data analysis and statistical modeling provides intellectual challenges with deep applications in almost every field of natural and social sciences and engineering. The field of nonparametric statistics has made a significant contribution to the success of science with algorithms that are hidden but critical even in the inner workings of cell phones. At a recent National Research Council workshop, numerous scientists identified critical statistical needs in their work with massive data sets: new dimension reduction algorithms, specialized visualization tools for exploring massive data, better clustering algorithms, and techniques for handling nonstationary data. Results from this proposed research directly impact three of these four critical opportunities.This program represents a comprehensive and long-term attack on a host of important data analytic problems in multivariate estimation.Graduate training is significant component of this project. The results will be of long-term theoretical interest and will provide short-term solutions to real-world problems.

随着新的数据收集技术的出现，对统计方法的需求已不断增长。 根据统计标准，许多结果数据集是不寻常的：巨大的和高度非线性的受污染。 有时，数据来自仅部分已知的机制。估计，测试，功能测试，模式发现，特征提取，可视化和比较的任务需要重新查看每个问题。在这些较高维度中，非参数方法已在一个维度和二维中广泛使用。将特别强调多元回归和密度估计问题，以及密切相关的应用，例如聚类，混合估计，模式识别，稳健估计和降低尺寸。 统计学家对科学方法的看法是一个不断改进的模型构建，数据收集，估计，批评和精炼的过程。但是，许多实践统计学家无法修复合适的模型。在这项研究中特别感兴趣的是提供关键诊断信息作为模型估计任务的一部分的方法。 这项研究的重点是基于数据的特定最小距离参数估计算法，该算法已针对其稳健性。该算法可以应用于混合模型和样条拟合。可以拟合不完整的密度模型，这是一个独特的功能，将在回归，图像处理，聚类，离群检测和密度估计的背景下进行充分探索。 用于功能数据分析的非参数方法将通过新颖的数据源设计和测试。其他应用程序包括自适应小波阈值，解决回归问题的解决方案的解决方案以及仅适用于数据的模型的应用。在数据分析和统计模型中研究的模型几乎在自然和社交领域的所有领域中都具有智力挑战。非参数统计的领域为科学的成功做出了重大贡献，即即使在手机的内部运作中，这些算法都隐藏但至关重要。 在最近的国家研究委员会研讨会上，许多科学家在其工作中确定了关键的统计需求：新的降低算法，专门的可视化工具，用于探索大量数据，更好的聚类算法以及用于处理非机构数据的技术。 这项拟议的研究的结果直接影响了这四个关键机会中的三个。该计划代表了对多元估计中许多重要数据分析问题的全面攻击。学习培训是该项目的重要组成部分。 结果将具有长期的理论利益，并将为现实世界中的问题提供短期解决方案。