Variable Selection and Parameter Estimation with the Atan Regularization Method

Algorithm 1

Iteratively reweighted Lasso (IRL) algorithm.

(1) Start with . Set and .

 Outer loop:

(2) Set and ;

(3) Increment and ;

(4) Update the weights: , ;

  Inner loop:

  Solve the Karush-Kuhn-Tucker (KKT) conditions for fixed :

  , if ,

  , if ,

(5) Goto Step (3);

(6) Repeat Steps (3)–(5) until .

  The estimate is the limit point of the outer loop, ;

(7) Decrement and . Return to (2) using as a warm start.