I'd like to know if the following explanation is a correct way to introduce Quantile regression to someone who just know OLS (the goal is just to give an intuition)
- Quantile regression minimise MAE instead of MSE so this is more robus to outlier.
- We can give more or less penalty to over estimation than under estimation.
For instance with Q=0.9, under estimation penalty is 9 times higher than over estimation penalty. In this case 90% of the distance between the dots and the regression line is under the line and 10% over the line.
- If we don't care about giving more penalty to over or under estimation we can use Q=0.5 and then we do a LAD regression. In this case 50% of the distance between the dots and the regression line is under the line and 50% over the line.
ps: Unfortunately we can obtain an infinite number of solution with this technique so we can ensure we really have 90% or 50% of residual over the regression line but that's the idea