This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via `1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.

Many traditional approaches to statistical analysis cease to be useful when the number of variables is large in comparison with the sample size. Penalized regression methods have proved to be an attractive approach, both theoretically and empirically, for dealing with these problems. This thesis focuses on the development of penalized regression methods for high-dimensional variable selection. ...

We propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions. Important applications include semiparametric linear regression with censored responses and semiparametric regression with missing predictors. Unlike the existing penalized maximum likelihood estimators, the proposed penalized estimating functions may not pert...

Increasingly amounts of biological data promote the development various penalized regression models. This review discusses recent advances in both linear and logistic models with penalization terms. is mainly focused on models, some corresponding optimization algorithms, their applications data. The pros cons different terms response prediction, sample classification, network construction featu...