Advances in Decision Sciences
Volume 2007 (2007), Article ID 24053, 13 pages
doi:10.1155/2007/24053
On Solving Lq-Penalized Regressions
Tracy Zhou Wu1
, Yingyi Chu2
and Yan Yu3
1JPMorgan Chase Bank, 1111 Polaris Pkwy, Columbus 43240, OH, USA
2ABN AMRO Bank, 250 Bishopsgate, London EC2M 4AA, UK
3Department of Quantitative Analysis and Operations Management, University of Cincinnati, P.O. Box 210130, Cincinnati 45221, OH, USA
Abstract
Lq-penalized regression arises in multidimensional statistical modelling where all or part of the regression coefficients are penalized to achieve both accuracy and parsimony of statistical models. There is often substantial computational difficulty except for the quadratic penalty case. The difficulty is partly due to the nonsmoothness of the objective function inherited from the use of the absolute value. We propose a new solution method for the general Lq-penalized regression problem based on space transformation and thus efficient optimization algorithms. The new method has immediate applications in statistics, notably in penalized spline smoothing problems. In particular, the LASSO problem is shown to be polynomial time solvable. Numerical studies show promise of our approach.