Achieving the oracle property of OEM with nonconvex penalties

ABSTRACT

Thepenalised least square estimator of non-convex penalties such as the smoothly clipped absolute deviation (SCAD) and the minimax concave penalty (MCP) is highly nonlinear and has many local optima. Finding a local solution to achieve the so-called oracle property is a challenging problem. We show that the orthogonalising EM (OEM) algorithm can indeed find such a local solution with the oracle property under some regularity conditions for a moderate but diverging number of variables.

KEYWORDS:

• EM algorithm
• non-convex optimisation
• penalised regression
• variable selection

Acknowledgments

We thank the editor, the associate editor, and two referees for their helpful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Xiong's research was supported by the National Natural Science Foundation of China [grant number 11471172], [grant number 11671386].