dantzigS function

Dantzig selector using the lpsolve package

The Dantzig selector (DS) finds a solution for the model parameters of a linear model, beta using linear programming. For a given delta, DS minimizes the L_1-norm (sum of absolute values) of beta subject to the constraint that max(|t(X)(y-X * beta)|)<= delta.

Source

Cand`es, E. and Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35 (6), 2313--2351.

Phoa, F. K., Pan, Y. H. and Xu, H. (2009). Analysis of supersaturated designs via the Dantzig selector. Journal of Statistical Planning and Inference 139 (7), 2362--2372.

dantzigS(X, y, delta, scale.X = 1)

Arguments

• X: a design matrix.
• y: a vector of responses.
• delta: the specific value of delta for which the Dantzig Selector optimization needs to be solved
• scale.X: a number by which each column of X should be scaled

Returns

A list containing the (a) opt (Value of objective function at optimum), (b) status (Numeric indicator: 0 = success, 2 = no feasible solution), (c) beta (the estimated values of beta), (d) delta