DIRECTION IDENTIFICATION AND MINIMAX ESTIMATION IN HIGH-DIMENSIONAL SPARSE REGRESSION VIA A GENERALIZED EIGENVALUE APPROACH
针对高维稀疏线性回归，通过约束参数向量的方向，利用广义特征值问题识别方向并估计参数，提出基于RIFLE算法的新估计量，在模拟中优于现有方法。
In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint $l_0$ on the direction of the parameter vector. We begin by establishing a general result that identifies this direction through the leading generalized eigenspace of specific measurable matrices. Using this result, we propose a novel approach to the selection of the best subsets by solving an empirical generalized eigenvalue problem to estimate the direction of the HD parameter. We then introduce a new estimator based on the RIFLE algorithm, providing a non-asymptotic bound for the estimation risk, minimax convergence, and a central limit theorem. Simulations demonstrate the superiority of our method over existing $l_0$ -constrained estimators.