Suchergebnisse

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.