文章基本信息

标题：On Solving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:math>-Penalized Regressions
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作者：Tracy Zhou Wu ; Yingyi Chu ; Yan Yu 等
期刊名称：Advances in Decision Sciences
印刷版ISSN：2090-3359
电子版ISSN：2090-3367
出版年度：2007
卷号：2007
DOI：10.1155/2007/24053
出版社：Hindawi Publishing Corporation
摘要：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.