Quantile regression

Summary

Quantile regression models a conditional quantile of a response, such as the conditional median, as a function of covariates. Where ordinary linear regression fits the conditional mean by least squares, quantile regression minimises an asymmetric absolute loss, the check function. Fitting several quantile levels shows how the whole conditional distribution changes with the covariates, not only its centre. Koenker and Bassett introduced it in 1978, and the median case is robust to outliers in the response.