An algorithm to find all regression quantiles

Abstract

Regression quantiles are a robust alternative to the popular least squares regression and provide good descriptive statistics for the data. The problem of determining all regression quantiles associated with a data set can be formulated as a parametric programming problem. We present a simple algorithm to solve the problem. The algorithm exploits the special structure of the problem. We illustrate the proposed algorithm with a simple example.

Keywords:

• L ₁ regression
• least absolute deviations
• least absolute errors
• linear programming
• minimum sum of absolute errors
• parametric programming