We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike’s information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.
"Model selection for high-dimensional linear regression with dependent observations." Ann. Statist. 48 (4) 1959 - 1980, August 2020. https://doi.org/10.1214/19-AOS1872