L1 for the simple linear regression model

By modifying the direct method to solve the overdetermined linear system we are able to present an algorithm for L₁ estimation which appears to be superior computationally to any other known algorithm for the simple linear regression problem.     

Least absolute value regression: a special case of piecewise linear minimization

The Barrodale and Roberts algorithm for least absolute value (LAV) regression and the algorithm proposed by Bartels and Conn both have the advantage that they are often able to skip across points at which the conventional simplex-method algorithms for LAV regression would be required to carry out an (expensive) pivot operation.

We indicate here that this advantage holds in the Bartels-Conn approach for a wider class of problems: the minimization of piecewise linear functions. We show how LAV regression, restricted LAV regression, general linear programming and least maximum absolute value regression can all be easily expressed as piecewise linear minimization problems.     

Consistency of l 1 estimates in censored linear regression models

In this paper, the regression model with a nonnegativity constraint on the dependent variable is considered. Under weak conditions, L ₁ estimates of the regression coefficients are shown to be consistent.     

Least Absolute Regression Revisited

We describe a method for fitting a least absolute residual (LAR) line through a set of two–dimensional points. The algorithm is based on a labeling technique derived from linear programming. It is suited for interactive data analysis and can be carried out with graph paper and a programmable hand calculator. Tests conducted with a Pascal program indicate that the algorithm is computationally efficient.     

Convergent estimators for the l1-median of banach valued random variable

Let E be a separable Banach space, which is the dual of a Banach space F. If X is an E-valued random variable, the set of L₁-medians of X is ArgminE[(d)]. Assume that this set contains only one element. From any sequence of probability measures {(d) 1} on E, which converges in law to X, we give two approximating sequences of the L₁-median, for the weak* topology induced by F.