COBRA: A Combined Regression Strategy

Abstract : A 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 nonparametric/nonlinear combined estimator is shown to perform asymptotically at least as well in the $L^2$ sense as the best combination of the basic estimators in the collective. 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.
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Submitted on : Thursday, May 23, 2019 - 7:44:57 AM
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Gérard Biau, Aurélie Fischer, Benjamin Guedj, James Malley. COBRA: A Combined Regression Strategy. Journal of Multivariate Analysis, Elsevier, 2016, ⟨10.1016/j.jmva.2015.04.007⟩. ⟨hal-01361789v3⟩

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