Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Tower Research Capital, New York, NY, USA
Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA
peterq@stat.wisc.edu
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.