Multivariate Nonparametric Methodology Studies

随着新的数据收集技术的出现，对统计方法的需求不断增长。以统计标准来看，这些数据集中的许多都是不寻常的：它们是海量的；它们是高度非线性的；它们被污染；它们包含实际上是函数的数据；或者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也适用于这些较高的维。特别强调多元回归和密度估计问题，以及与之密切相关的应用，如聚类、混合估计、模式识别、稳健估计和降维。统计学家对科学方法的看法是一个不断改进的过程，包括建模、数据收集、估计、批评和改进。然而，许多执业统计学家因无法修复不合适的模型而受阻。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。研究的重点是一种相对较新的基于最小距离数据的参数估计算法，它的稳健性已经得到了研究。该算法可以应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、离群点检测和密度估计的背景下得到充分探索。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，以及应用于仅适用于数据子集的模型。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的能力。其他新的潜在应用包括自适应小波阈值，解决混合回归问题，以及应用于仅适用于数据子集的模型。数据分析和统计建模的研究提供了智力挑战，在自然科学、社会科学和工程的几乎所有领域都有深入的应用。非参数统计领域为科学的成功做出了重大贡献，其算法是隐藏的，但即使在手机的内部工作中也是关键的。在国家研究委员会最近的一次研讨会上，许多科学家确定了他们在处理海量数据时的关键统计需求：新的降维算法、用于探索海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。这项拟议研究的结果直接影响到这四个关键机会中的三个。该计划代表了对多变量估计中的许多重要数据分析问题的全面和长期的攻击。研究生培训是该项目的重要组成部分。这一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.