An Algorithm to Find all Regression Quantiles Using Bicriteria Optimization

SYNOPTIC ABSTRACT

Regression quantiles are a robust alternative to the popular least squares regression, and provide good descriptive statistics for the data. Our objectives in this paper are (i) to show that the problem “determine all regression quantiles associated with a data set” can be formulated as a bicriteria linear programming problem, and (ii) to present a simple algorithm which combines parametric programming with the simplex algorithm and exploits the special problem structure to solve that problem. We illustrate the proposed algorithm with a simple example.

Key Words and Phrases:

• L₁ regression
• least absolute deviations
• least absolute errors
• linear programming
• minimum sum of absolute errors