The Dantzig Selector in Cox's Proportional Hazards Model

The Dantzig Selector in Cox’s Proportional Hazards Model

The Dantzig Selector is a recent approach to estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression coefficients exactly to zero, thus performing variable selection. However, such a framework, contra...

The Group Dantzig Selector

We introduce a new method — the group Dantzig selector — for high dimensional sparse regression with group structure, which has a convincing theory about why utilizing the group structure can be beneficial. Under a group restricted isometry condition, we obtain a significantly improved nonasymptotic `2-norm bound over the basis pursuit or the Dantzig selector which ignores the group structure. ...

The Dantzig Selector : Statistical Estimation

given just a single parameter t. Two active-set methods were described in [11], with some concern about efficiency if p were large, where X is n× p . Later when basis pursuit de-noising (BPDN) was introduced [2], the intention was to deal with p very large and to allow X to be a sparse matrix or a fast operator. A primal–dual interior method was used to solve the associated quadratic program, b...

Multi-Stage Dantzig Selector

We consider the following sparse signal recovery (or feature selection) problem: given a design matrix X ∈ Rn×m (m À n) and a noisy observation vector y ∈ R satisfying y = Xβ∗ + 2 where 2 is the noise vector following a Gaussian distribution N(0, σI), how to recover the signal (or parameter vector) β∗ when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery w...

Discussion of “the Dantzig selector”