Multivariate Nonparametric Methodology Studies

多元非参数方法研究

• 批准号: 0505584
• 负责人: David Scott
• 金额: --
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505584&HistoricalAwards=false
• 关键词: Multivariate; Nonparametric; Methodology; Studies

The demands on statistical methodology have grown relentlesslyas new technologies for data collection appear. Many ofthese datasets are unusual by statistical standards:they are massive; they are highly nonlinear; they arecontaminated; they contain data which are in fact functions;or the data come from a mechanism which is only partially known.The tasks of estimation, testing, functional testing, patterndiscovery, feature extraction, visualization, and comparisonrequire the statistician look at each problem anew.Nonparametric methodology, which has been widely used in oneand two dimensions, is also appropriate in these higher dimensions.Particular emphasis will be given to multivariate regression anddensity estimation problems, and closely related applications suchas clustering, mixture estimation, pattern recognition, robustestimation, and dimension reduction. The statistician's view ofthe scientific method is a continuously improving process of modelbuilding, data collection, estimation, criticism, and refinement.However, many practicing statisticians are stymied by an inabilityto repair poorly fitting models. Of particular interest in thisresearch are methods which provide critical diagnostic informationas part of the model estimation task. A focus of this research isa relatively new minimum-distance data-based parametric estimationalgorithm, 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 highly unusualcapability that will be explored fully in the context of regression,image processing, clustering, outlier detection, and densityestimation. Other novel potential applications include adaptivewavelet thresholding, solution of the mixture of regression problems,and application to models which apply to only a subset of the data.capability that will be explored fully in the context of regression, image processing, clustering, outlier detection, and density estimation. Other novel potential 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 providesintellectual challenges with deep applications in almost everyfield of natural and social sciences and engineering. The field ofnonparametric statistics has made a significant contribution tothe success of science with algorithms that are hidden but criticaleven in the inner workings of cell phones. At a recent NationalResearch Council workshop, numerous scientists identifiedcritical statistical needs in their work with massive data sets:new dimension reduction algorithms, specialized visualization toolsfor exploring massive data, better clustering algorithms, andtechniques for handling nonstationary data. Results from this proposedresearch directly impact three of these four critical opportunities.This program represents a comprehensive and long-term attackon 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.

随着数据收集新技术的出现，对统计方法的要求不断增长。按照统计标准，这些数据集中有许多是不寻常的：它们非常庞大；它们是高度非线性的；他们被污染;它们包含的数据实际上是函数；或者数据来自于我们只知道一部分的机制。估计、测试、功能测试、模式发现、特征提取、可视化和比较等任务要求统计学家重新审视每个问题。在一维和二维中广泛使用的非参数方法同样适用于这些高维。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，如聚类、混合估计、模式识别、鲁棒估计和降维。统计学家对科学方法的看法是一个不断改进的过程，包括建立模型、收集数据、估计、批评和改进。然而，许多执业统计学家由于无法修复不合适的模型而受到阻碍。本研究特别感兴趣的是提供关键诊断信息的方法，作为模型估计任务的一部分。本研究的一个重点是相对较新的基于最小距离数据的参数估计算法，并对其鲁棒性进行了研究。该算法可用于混合模型和样条拟合。可以拟合不完全密度模型，这是一种非常不寻常的能力，将在回归、图像处理、聚类、离群值检测和密度估计的背景下进行充分探索。其他新的潜在应用包括自适应小波阈值化，混合回归问题的解决方案，以及仅适用于数据子集的模型的应用。这些功能将在回归，图像处理，聚类，离群值检测和密度估计的背景下进行充分探索。其他新的潜在应用包括自适应小波阈值，混合回归问题的解决方案，以及仅适用于数据子集的模型的应用。数据分析和统计建模的研究为自然科学、社会科学和工程的几乎每个领域提供了深入应用的智力挑战。非参数统计领域对科学的成功做出了重大贡献，其算法隐藏但至关重要，甚至在手机的内部工作中也是如此。在最近的一次国家研究委员会研讨会上，许多科学家确定了他们在大量数据集工作中的关键统计需求：新的降维算法，用于探索大量数据的专门可视化工具，更好的聚类算法，以及处理非平稳数据的技术。这项研究的结果直接影响了这四个关键机会中的三个。这个程序代表了一个全面和长期的攻击主机的重要数据分析问题，在多元估计。研究生培训是这个项目的重要组成部分。研究结果将具有长期的理论价值，并将为现实世界的问题提供短期的解决方案。