Curve aggregation and classification

曲线聚合和分类

• 批准号: 0406049
• 负责人: Florentina Bunea
• 金额: $ 16.13万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0406049&HistoricalAwards=false
• 关键词: Curve; aggregation; classification

This research is devoted to aggregation of estimators in nonparametricregression models. The motivation is twofold. One is the existenceof many different methods of estimation, leading to possibly competingestimators. In this case one may want to combine the estimators, ratherthan to select them. The second one arises in meta-analysis type problems,in which one wishes to aggregate estimators obtained from differentsamples. This research proposes a readily implementable method that addressesthese questions, using tools from the theories of empirical processes, minimaxadaptive estimation and optimization. The proposed procedure yields, viaan oracle inequality, minimax optimal aggregation bounds for the risk of theestimators.This proposal has immediate applications in seismology and clinicalpsychology and, more widely, to any data set that is comprised of curves.The methods proposed here are used to develop signature curves for eventsof interest. Having a signature for a seismic wave allows quickdiscrimination between earthquakes and waves produced by man inducedexplosions. An EEG based signature for depression will improve accuracy indiagnosing the disease and will permit nuanced classification of furtherpatients, according to the severity of the illness. The software that allowsthese analyzes will be made freely available on the world wide web, alongwith a step by step description that will facilitate its use by researchersfrom other disciplines.

本文研究非参数回归模型中估计量的集结问题。动机是双重的。 一个是存在许多不同的估计方法，导致可能competingestimators。在这种情况下，人们可能希望联合收割机的估计，而不是选择他们。第二个问题出现在元分析类型的问题，其中一个希望聚合从不同的样本获得的估计。本研究提出了一个易于实施的方法，解决这些问题，使用的工具，从理论的经验过程，最小最大自适应估计和优化。本文提出的方法通过Oracle不等式得到了估计量风险的极小极大最优聚集界，该方法在地震学和临床心理学中有直接的应用，更广泛地应用于任何由曲线组成的数据集，本文提出的方法可用于生成感兴趣事件的特征曲线。有了地震波的特征，就可以快速区分地震和人为爆炸产生的地震波。基于脑电图的抑郁症特征将提高诊断疾病的准确性，并将允许根据疾病的严重程度对进一步的患者进行细致的分类。允许这些分析的软件将在万维网上免费提供，并附有一步一步的描述，以方便其他学科的研究人员使用。