M-estimation and model identification based on double SCAD penalization

Jianhua Hu and NengHui Zhu

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 23, 5639-5661

Abstract: M-estimation is a widely used method for robust statistical inference. In this article, using a B-spline series approximation with a double smoothly clipped absolute deviation penalization, we solve the problem of simultaneous variable selection and parametric component identification in a non parametric additive model. The theoretical properties of the double non concave penalized M-estimation are established. The proposed approach is resistant to heavy-tailed errors or outliers in the responses. Simulation studies for finite-sample cases are conducted and a real dataset is also analyzed for illustration of this new approach.

Date: 2018
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DOI: 10.1080/03610926.2017.1400055

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