Abstract : This paper investigates the problem of selection and estimation in a high dimensional regression-type model. We propose a procedure with no optimization called LOL, for Learning Out of Leaders. LOL is an auto-driven algorithm with two thresholding steps. A first adaptive thresholding helps to select leaders among the initial regressors in such a way to reduce the dimensionality. Then a second thresholding follows the estimations and predictions performed by linear regression on the leaders. Theoretical results are proved. As an estimation procedure, LOL is optimal since the upper exponential bounds are achieved. Rates of convergence are provided and show that LOL is also consistent as a selection procedure. An extensive computational experiment is conducted to emphasize the practical good performances of LOL.