Curve aggregation and classification

本文主要研究非参数回归模型中估计的集结问题。动机是双重的。其一是存在许多不同的估计方法，导致可能存在相互竞争的估计者。在这种情况下，人们可能想要组合估计器，而不是选择它们。第二个问题出现在Meta分析类型的问题中，在这个问题中，人们希望聚合从不同样本获得的估计量。这项研究提出了一种易于实施的方法，利用经验过程、最小自适应估计和最优化理论的工具来解决这些问题。该方法得到了估计器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，更广泛地适用于任何由曲线组成的数据集。本文提出的方法被用来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波。基于脑电的抑郁症信号将提高诊断疾病的准确性，并将根据疾病的严重程度对进一步的患者进行细微差别的分类。支持这些分析的软件将在万维网上免费提供，并附一份循序渐进的说明，以方便其他学科的研究人员使用。

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.