  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.
