Curve aggregation and classification

Florida State University, Tallahassee FL

Investigators

Abstract

This research is devoted to aggregation of estimators in nonparametric regression models. The motivation is twofold. One is the existence of many different methods of estimation, leading to possibly competing estimators. In this case one may want to combine the estimators, rather than to select them. The second one arises in meta-analysis type problems, in which one wishes to aggregate estimators obtained from different samples. This research proposes a readily implementable method that addresses these questions, using tools from the theories of empirical processes, minimax adaptive estimation and optimization. The proposed procedure yields, via an oracle inequality, minimax optimal aggregation bounds for the risk of the estimators. This proposal has immediate applications in seismology and clinical psychology and, more widely, to any data set that is comprised of curves. The methods proposed here are used to develop signature curves for events of interest. Having a signature for a seismic wave allows quick discrimination between earthquakes and waves produced by man induced explosions. An EEG based signature for depression will improve accuracy in diagnosing the disease and will permit nuanced classification of further patients, according to the severity of the illness. The software that allows these analyzes will be made freely available on the world wide web, along with a step by step description that will facilitate its use by researchers from other disciplines.