An Algorithm to Find all Regression Quantiles Using Bicriteria Optimization

摘要

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 #x201c;determine all regression quantiles associated with a data set#x201d; 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.