- COmponent Selection and Selection Operator for multivariate smoothing splines

COSSO, the short term for Component Selection and Smoothing Operator, is a new regularization method developed by Lin and Zhang (2006) in the multivariate smoothing splines for simultaneous function selection and smoothing. Different from traditional splines where a rough penalty is often used for function smoothing, the COSSO imposes a soft-thresholding penalty operator on function components in the framework of reproducing kernel Hilbert space (RKHS), which simultaneously achieves function selection and smoothing. In a sense, the COSSO generalizes LASSO (Tibshirani 1996), a powerful shrinkage method for variable selection in linear models, to the context of nonparametric smoothing models.

- Component Selection and Smoothing in Multivariate Nonparametric Regression
Lin, Y. and Zhang, H. H. (2006)
*Annals of Statistics*34 (5), 2272-2297. - Component Selection and Smoothing for Nonparametric Regression in Exponential Families. Zhang, H. H. and Lin, Y (2006)
*Statistica Sinica,*16, 1021-1042. - Variable Selection for Support Vector Machines via Smoothing Spline ANOVA. Zhang, H. H. (2006)
*Statistica Sinica,*16(2), 659-674. - Nonparametric Model Selection in Hazard Regression. Leng, C. and Zhang, H. H. (2007)
*Journal of Nonparametric Statistics*, 18(7), 417 - 429. - The adaptive COSSO for nonparametric surface estimation and model selection. Storlie, C., Bondell, H., Reich, B. and Zhang, H. H. (2010)
*Statistica Sinica*, to appear.

The COSSO solution can be found by iteratively solving the standard smoothing splines and the non-negative garrote problem.

This material is based upon work supported by the National Science Foundation. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).