Multivariate Nonparametric Methodology Studies

随着新的数据收集技术的出现，对统计方法的需求也在不断增长。 许多这样的数据集在统计标准下是不寻常的：它们是巨大的;它们是高度非线性的;它们被污染了;它们包含的数据实际上是函数;或者数据来自于一个仅仅部分已知的机制。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要求统计学家重新审视每个问题。非参数方法，已广泛用于一维和二维，也适用于这些更高的维度。特别强调将给予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，robustestimation，和降维。 统计学家对科学方法的看法是，建立模型、收集数据、估计、批评和改进的过程是不断改进的。然而，许多实践中的统计学家却被无法修复拟合不佳的模型所困扰。在这项研究中特别感兴趣的是作为模型估计任务的一部分提供关键诊断信息的方法。 本研究的一个重点伊萨一个相对较新的基于最小距离数据的参数估计算法，它的鲁棒性已被研究，该算法可以应用于混合模型和样条拟合，一个不完整的密度模型可以拟合，一个非常不寻常的能力，将在回归，图像处理，聚类，离群点检测和密度估计的背景下充分探索。 其他新的潜在应用包括adaptivewavelet thresholding，回归问题的混合物的解决方案，和应用程序的模型，适用于只有一个子集的数据。能力，将充分探讨的背景下，回归，图像处理，聚类，离群值检测和密度估计。 其他新的潜在应用包括自适应小波阈值，回归问题的混合解决方案，并应用于模型，适用于只有一个子集的data.Research在数据分析和统计建模providesintellectual挑战与深入的应用在几乎所有领域的自然和社会科学和工程。非参数统计学领域对科学的成功做出了重大贡献，它的算法是隐藏的，但即使在手机的内部工作中也是至关重要的。 在最近的国家研究理事会研讨会上，许多科学家确定了他们在处理海量数据集时的关键统计需求：新的降维算法，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。 从这个proposedresearch的结果直接影响这四个关键opportunity.This程序中的三个代表了一个全面的和长期的攻击在多变量估计的一系列重要的数据分析问题.研究生培训是该项目的重要组成部分。 这些结果将具有长期的理论意义，并将为现实世界的问题提供短期的解决方案。

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.