  This paper investigates the estimation problem in a regression-type model. To
be able to deal with potential high dimensions, we provide a procedure called
LOL, for Learning Out of Leaders with no optimization step. LOL is an
auto-driven algorithm with two thresholding steps. A first adaptive
thresholding helps to select leaders among the initial regressors in order to
obtain a first reduction of dimensionality. Then a second thresholding is
performed on the linear regression upon the leaders. The consistency of the
procedure is investigated. Exponential bounds are obtained, leading to minimax
and adaptive results for a wide class of sparse parameters, with (quasi) no
restriction on the number p of possible regressors. An extensive computational
experiment is conducted to emphasize the practical good performances of LOL.
