An Algorithm to Select the Best Subset for a Least Absolute Value Regression Problem

摘要

This paper considers the problem of obtaining the best subset of regressors under a least absolute value criterion. The model is the classic linear regression model with m explanatory variables and a dependent variable. The importance of the explanatory variables is measured by obtaining the minimum sum of absolute deviations when only k of the m explanatory variables are included in the model. An algorithm is presented to obtain the 'best' subset of size k, k = 1,...,m. Several algorithms to solve the best subset problem are available when the criterion for evaluation is least squares. However, recently statisticians have become increasingly aware of the limitations of least squares and have popularized 'robust-resistant' estimation techniques. Least absolute values is such a technique. Special purpose computer codes which utilize the simplex algorithm of linear programming are used to solve the least absolute value regression problem. This paper incorporates two of these specialized codes within a branch-and-bound algorithm to solve the best subset problem.