Assi N'GUESSAN ; Ibrahim Sidi Zakari ; Assi Mkhadri - A mixture of local and quadratic approximation variable selection algorithm in nonconcave penalized regression

arima:1962 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 29, 2013, Volume 16, 2012 - https://doi.org/10.46298/arima.1962
A mixture of local and quadratic approximation variable selection algorithm in nonconcave penalized regression

Authors: Assi N'GUESSAN ; Ibrahim Sidi Zakari ; Assi Mkhadri

We consider the problem of variable selection via penalized likelihood using nonconvex penalty functions. To maximize the non-differentiable and nonconcave objective function, an algorithm based on local linear approximation and which adopts a naturally sparse representation was recently proposed. However, although it has promising theoretical properties, it inherits some drawbacks of Lasso in high dimensional setting. To overcome these drawbacks, we propose an algorithm (MLLQA) for maximizing the penalized likelihood for a large class of nonconvex penalty functions. The convergence property of MLLQA and oracle property of one-step MLLQA estimator are established. Some simulations and application to a real data set are also presented.


Volume: Volume 16, 2012
Published on: August 29, 2013
Submitted on: January 29, 2013
Keywords: Regression, Variable selection, SCAD penalty, LARS, LLA and LQA algorithms.,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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