Title: Direction identification and minimax estimation by generalized eigenvalue problem in high dimensional sparse regression Authors:  Mathieu Sauvenier - Universite Catholique de Louvain (Belgium) [presenting]
Sebastien Van Bellegem - Universite catholique de Louvain (Belgium)
Abstract: In high-dimensional sparse linear regression, the selection and the estimation of the parameters are studied based on an $l_0-$constraint on the direction of the vector of parameters. A general result for the direction of the vector of parameters is first established, which is identified through the leading generalized eigenspace of measurable matrices. Based on this result, addressing the best subset selection problem is suggested from a new perspective by solving an empirical generalized eigenvalue problem to estimate the direction of the high-dimensional vector of parameters. A new estimator is then studied based on the RIFLE algorithm and demonstrates a non-asymptotic bound of the $L^2$ risk, the minimax convergence of the estimator and a central limit theorem. Simulations show the superiority of the proposed inference over some known $l_0$ constrained estimators.