Multivariate Nonparametric Methodology Studies

多元非参数方法研究

• 批准号: 0204723
• 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: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2005-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204723&HistoricalAwards=false
• 关键词: Multivariate; Nonparametric; Methodology; Studies

Proposal ID: DMS-0204723PI: David ScottTitle: Multivariate nonparametric methodology studiesThe investigators will study new nonparametric methodology focusing on the mid-range and high-range dimensions to better understand data modeling, the curse of dimensionality, and problems associated with massive data sets in multivariate regression and density estimation as well as closely related problems in clustering, mixtures, pattern recognition, and dimension reduction. A new data-based parametric estimation algorithm, based upon integrated squared error, will be investigated for its flexibility and robustness. By applying the criterion to the fitting of local polynomials, a new robust nonparametric regression algorithm can be proposed, which will be applied to automatic detection of hundreds of overlapping tracks in subatomic detector experiments. This project will examine semiparametric models for density estimation that can work better than ordinary nonparametric algorithms, extending feasibility by several extra dimensions. Of special interest, this algorithm can be used to fit subsets of a full mixture model. Applications include regression, image processing, clustering, outlier detection, density estimation, and visualization. The project will extend work on spatial modeling and the combination of multiple data surveys into useful data modeling and maps of conditional estimators of factors and their covariates. Currently, simultaneous mapping of variables is difficult to interpret, due to the availability of data only in discrete spatial areas (e.g. census tracts) and cross-tabulation of the two variables of interest. By constructing a smooth map of one variable as a second variable varies, a more faithful and accurate understanding of the spatial relationship may be obtained.Nonparametric methodology is widely used in one and two dimensions, but less so in higher dimensions. This research focuses on the mid-range and high-range dimensions and provides a deeper understanding of the implications to data modeling of the curse of dimensionality and problems associated with massive data sets. Particular emphasis will be given to multivariate regression and density estimation problems, and closely related applications such as clustering, mixture estimation, pattern recognition, and dimension reduction. This proposal examines new points of view, especially related to locally adaptive and spatial estimation, as well as some recent extensions of nonparametric criteria to parametric problems. The new parametric approach has potential for new nonparametric formulations and applications. At a recent National Research Council workshop, numerous scientists identified critical statistical needs in their work with massive data sets: alternatives to principal components, specialized visualization tools for exploring massive data, better clustering algorithms, and techniques for handling nonstationary data. Results from this 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. The results will be of long-term theoretical interest and will provide near-term solutions to real-world problems.

提案 ID：DMS-0204723PI：David Scott 标题：多元非参数方法研究研究人员将研究新的非参数方法，重点关注中范围和高范围维度，以更好地理解数据建模、维数灾难以及与海量数据集相关的问题。多元回归和密度估计以及聚类、混合、模式识别和降维中密切相关的问题。将研究一种基于积分平方误差的新的基于数据的参数估计算法的灵活性和鲁棒性。通过将该准则应用于局部多项式的拟合，可以提出一种新的鲁棒非参数回归算法，该算法将应用于亚原子探测器实验中数百个重叠轨迹的自动检测。该项目将研究用于密度估计的半参数模型，该模型比普通非参数算法效果更好，从而通过几个额外的维度扩展了可行性。特别有趣的是，该算法可用于拟合完全混合模型的子集。应用包括回归、图像处理、聚类、异常值检测、密度估计和可视化。该项目将把空间建模和多个数据调查的组合工作扩展到有用的数据建模和因素及其协变量的条件估计图。 目前，由于数据仅在离散空间区域（例如人口普查区）和两个感兴趣的变量的交叉制表中可用，因此变量的同步映射很难解释。 通过构建一个变量随第二个变量变化的平滑映射，可以获得对空间关系的更忠实和准确的理解。非参数方法在一维和二维中广泛使用，但在更高维度中应用较少。这项研究重点关注中范围和高范围的维度，并提供对维度灾难和与海量数据集相关问题的数据建模的影响的更深入的理解。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、模式识别和降维。该提案研究了新的观点，特别是与局部自适应和空间估计相关的观点，以及非参数标准对参数问题的一些最新扩展。新的参数方法具有新的非参数公式和应用的潜力。在最近的国家研究委员会研讨会上，许多科学家确定了海量数据集工作中的关键统计需求：主成分的替代方案、用于探索海量数据的专用可视化工具、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这四个关键机会中的三个。该程序代表了对多元估计中许多重要数据分析问题的全面和长期的攻击。研究结果将具有长期的理论意义，并将为现实世界的问题提供近期的解决方案。