Multivariate Nonparametric Methodology Studies

随着数据收集新技术的出现，对统计方法的要求不断增长。 从统计标准来看，其中许多数据集都是不寻常的：它们非常庞大； 它们是高度非线性的； 它们被污染了； 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要求统计学家重新审视每个问题。非参数方法已在一维和二维中广泛使用，也适用于这些更高的维度。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、稳健估计和降维。 统计学家对科学方法的看法是模型构建、数据收集、估计、批评和完善的不断改进的过程。然而，许多统计学家因无法修复拟合不佳的模型而陷入困境。这项研究特别感兴趣的是提供关键诊断信息作为模型估计任务一部分的方法。 本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，对其鲁棒性特性进行了研究。该算法可应用于混合模型和样条拟合。可以拟合不完整的密度模型，这是一种非常不寻常的功能，将在回归、图像处理、聚类、异常值检测和密度估计的背景下充分探索。 其他新颖的潜在应用包括自适应小波阈值、回归问题混合的解决方案以及仅适用于数据子集的模型的应用。将在回归、图像处理、聚类、异常值检测和密度估计的背景下充分探索该功能。 其他新颖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的深入应用提供了智力挑战。非参数统计领域通过隐藏但至关重要的算法为科学的成功做出了重大贡献，即使在手机的内部运作中也是如此。 在最近的国家研究委员会研讨会上，许多科学家确定了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。 这项拟议研究的结果直接影响这四个关键机会中的三个。该计划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。研究生培训是该项目的重要组成部分。 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.