Hard thresholding regression.

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.