Multivariate Nonparametric Methodology Studies

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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.