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MODEL SELECTION FOR HIGH-DIMENSIONAL LINEAR REGRESSION WITH DEPENDENT OBSERVATIONS
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MODEL SELECTION FOR HIGH-DIMENSIONAL LINEAR REGRESSION WITH DEPENDENT OBSERVATIONS
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Journal Article
MODEL SELECTION FOR HIGH-DIMENSIONAL LINEAR REGRESSION WITH DEPENDENT OBSERVATIONS
2020
Overview
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.
Publisher
Institute of Mathematical Statistics
Subject
