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Penalized composite quasi-likelihood for ultrahigh dimensional variable selection

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Abstract:

Summary. 

In high dimensional model selection problems, penalized least square approaches have been extensively used. The paper addresses the question of both robustness and efficiency of penalized model selection methods and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L1-penalty. It is completely data adaptive and does not require prior knowledge of the error distribution. The weighted L1-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias that is caused by the L1-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the method proposed that has both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1L2, and an optimal composite quantile method and evaluate their performance in both simulated and real data examples.

Keywords: Composite quasi-maximum likelihood estimation; Lasso; Model selection; Non-polynomial dimensionality; Oracle property; Robust statistics; Smoothly clipped absolute deviation

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2010.00764.x

Affiliations: 1: Princeton University, USA 2: University of Texas Health Science Center, Houston, USA

Publication date: June 1, 2011

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