Model selection for high-dimensional linear regression with dependent observations

Ching-Kang Ing

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arXiv · 1906.07395

Model selection for high-dimensional linear regression with dependent observations

Ching-Kang Ing

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Abstract

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.

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stat.ML cs.LG math.ST stat.TH

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BibTeX RIS

Ching-Kang Ing. 2019-06-18. Model selection for high-dimensional linear regression with dependent observations. https://arxiv.org/abs/1906.07395

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