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Achieving the oracle property of OEM with nonconvex penalties

Author

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  • Shifeng Xiong
  • Bin Dai
  • Peter Z. G. Qian

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.

Suggested Citation

  • Shifeng Xiong & Bin Dai & Peter Z. G. Qian, 2017. "Achieving the oracle property of OEM with nonconvex penalties," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 28-36, January.
    • Handle: RePEc:taf:tstfxx:v:1:y:2017:i:1:p:28-36
    DOI: 10.1080/24754269.2017.1326079
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    Cited by:

    1. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    2. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2022. "Penalized wavelet estimation and robust denoising for irregular spaced data," Computational Statistics, Springer, vol. 37(4), pages 1621-1651, September.

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