expectiles, M-quantile Regression, Asymmetric Least Squares

[josef...@gmail.com]

All we need is a new asymmetric RobustNorm, and we can get the
M-estimator analog of quantile regression, asymmetric LS and
M-quantiles.


as a quick check:
The plot compares QuantileRegression with M-Quantile regression using
asymmetric HuberT norm as a local differentiable or smooth
approximation to the "check" function.


(Expectiles and M-quantiles seem to become popular in finance and
other fields for risk analysis. The regression just penalizes positive
and negative residuals with different weights.)


Josef
(It's all the same, just different...)