Recursive Algorithm for L1 Norm Estimation in Linear Models

Abstract

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which is based on Dikin's method. The method can be considered as an appropriate alternative for the classical simplex method, which is sometimes time-consuming. The proposed method, compared with the simplex method, is thus easier for implementation and faster in performance. Furthermore, a recursive form of the Dikin's method is derived, which resembles the recursive least-squares method. Two simulated numerical examples show that the proposed algorithm gives as accurate results as the simplex method but in considerably less time. When dealing with a large number of observations, this algorithm can thus be used instead of the iteratively reweighted least-squares method and the simplex method.