The Lasso, proposed by Tibshirani (1996), is an acronym for Least Absolute Shrinkage and Selection Operator. Among the main reasons why it has become very popular for high-dimensional estimation problems are its statistical accuracy for prediction and variable selection coupled with its computational feasibility. Furthermore , since the Lasso is a penalized likelihood approach, the method is rather general and can be used in a broad variety of models. In the simple case of a linear model with orthonormal design, the Lasso equals the soft thresholding estimator models is the core example to develop the methodology for 1-penalization in high-dimensional settings. We discuss in this chapter some fundamental methodological and computational aspects of the Lasso. We also present the adaptive Lasso, an important two-stage procedure which addresses some bias problems of the Lasso. The methodological steps are supported by describing various theoretical results which will be fully developed in Chapters 6 and 7.
CITATION STYLE
Bühlmann, P., & van de Geer, S. (2011). Lasso for linear models (pp. 7–43). https://doi.org/10.1007/978-3-642-20192-9_2
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