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COBRA: A Nonlinear Aggregation Strategy

By Gérard Biau, Aurélie Fischer, Benjamin Guedj and James Malley

Abstract

40 pages, 5 tables, 12 figuresA new method for combining several initial estimators of the regression function is introduced. Instead of building a linear or convex optimized combination over a collection of basic estimators $r_1,\dots,r_M$, we use them as a collective indicator of the proximity between the training data and a test observation. This local distance approach is model-free and very fast. More specifically, the resulting collective estimator is shown to perform asymptotically at least as well in the $L^2$ sense as the best basic estimator in the collective. Moreover, it does so without having to declare which might be the best basic estimator for the given data set. A companion R package called \cobra (standing for COmBined Regression Alternative) is presented (downloadable on \url{http://cran.r-project.org/web/packages/COBRA/index.html}). Substantial numerical evidence is provided on both synthetic and real data sets to assess the excellent performance and velocity of our method in a large variety of prediction problems

Topics: Regression estimation, Aggregation, Nonlinearity, Consistency, Prediction, 62G05, 62G20, [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], [ STAT.ME ] Statistics [stat]/Methodology [stat.ME]
Publisher: HAL CCSD
Year: 2013
OAI identifier: oai:HAL:hal-01361789v2
Provided by: Hal-Diderot

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