Dantzig selector in linear models in n<p problems

Abstract

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. In radiology and biomedical imaging, for instance, one is typically able to collect far fewer measurements about an image of interest than the unknown number of pixels. Examples in functional MRI and tomography all come to mind. High dimensional data frequently arise in genomics. Gene expression studies are a typical example: a relatively low number of observations (in the tens) is available, while the total number of genes assayed (and considered as possible regressors) is easily in the thousands. Other examples in statistical signal processing and nonparametric estimation include the recovery of a continuous-time curve or surface from a finite number of noisy samples.