Expectile
In the mathematical theory of probability, the expectiles of a probability distribution are related to the expected value of the distribution in a way analogous to that in which the quantiles of the distribution are related to the median.
For, the expectile of the probability distribution with cumulative distribution function is characterized by any of the following equivalent conditions:
Quantile regression minimizes an asymmetric loss.
Analogously, expectile regression minimizes an asymmetric loss :
where is the Heaviside step function.