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Hard thresholding regression
Qiang Sun1, Bai Jiang2, Hongtu Zhu3
1Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada.
Abstract:
In this paper, we propose the hard thresholding regression (HTR) for estimating high-dimensional sparse linear regression models. HTR uses a two-stage convex algorithm to approximate the ℓ 0-penalized regression: The first stage calculates a coarse initial estimator, and the second stage identifies the oracle estimator by borrowing information from the first one. Theoretically, the HTR estimator achieves the strong oracle property over a wide range of regularization parameters. Numerical examples and a real data example lend further support to our proposed methodology.
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