Curve aggregation and classification

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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.