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 SCOTTTITLE：多元非参数方法论研究人员将研究研究人员的新非参数方法论，重点是中距离和高范围维度，以更好地了解数据建模，以及与大规模数据相关的大量群众群体概述，以及与群集的群体相关的问题，以及群集逐渐差异的问题，以及群集繁重的概述，以及群集繁重的概述，以及群集繁重的估算。识别和降低维度。基于集成平方误差的新的基于数据的参数估计算法将根据其灵活性和鲁棒性进行研究。通过将标准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，该算法将用于自动检测亚原子检测器实验中数百个重叠的轨道。该项目将检查半参数模型的密度估计，该密度估计可以比普通的非参数算法更好，从而将可行性扩展到了几个额外的维度。该算法特别感兴趣，可用于拟合完整混合模型的子集。应用包括回归，图像处理，聚类，离群检测，密度估计和可视化。该项目将扩展有关空间建模的工作，并将多个数据调查的组合扩展为有用的数据建模和因素及其协变量的条件估计量的图。 当前，由于仅在离散空间区域（例如人口普查区）和两个感兴趣的两个变量的交叉映射中，因此很难解释变量的同时映射。 通过构建一个变量的平滑映射作为第二个变量，可以获得对空间关系的更忠实，更准确的理解。Nononparametric方法论在一个和二维中广泛使用，但在更高的维度中却较少。这项研究的重点是中距离和高范围维度，并更深入地理解了对数据建模的含义以及与大规模数据集有关的诅咒和问题。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，模式识别和降低尺寸，将特别强调。该提案研究了新的观点，特别是与局部自适应和空间估计有关的观点，以及一些非参数标准到参数问题的一些扩展。新的参数方法具有新的非参数配方和应用的潜力。在最近的国家研究委员会研讨会上，许多科学家在使用大量数据集的工作中确定了关键的统计需求：主要组件的替代方案，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用于处理非机构数据的技术。这项研究的结果直接影响了这四个关键机会中的三个。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攻击。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近期解决方案。