Quantile estimators with orthogonal pinball loss function

To guarantee stable quantile estimations even for noisy data, a novel loss function and novel quantile estimators are developed, by introducing the effective concept of orthogonal loss considering the noise in both response and explanatory variables. In particular, the pinball loss used in classical quantile estimators is improved into novel orthogonal pinball loss (OPL) by replacing vertical loss by orthogonal loss. Accordingly, linear quantile...