Resumen de Regularization in statistics

Peter J Bickel, Bo Li, Alexandre B. Tsybakov, Sara van de Geer, Bin Yu, Teófilo Valdés Sánchez, Carlos Rivero Rodríguez, Jianqing Fan, Aad van der Vaart

• This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it. We have tried to focus on the importance of regularization when dealing with today's high-dimensional objects: data and models. A wide range of examples are discussed, including nonparametric regression, boosting, covariance matrix estimation, principal component estimation, subsampling.