Canonical quantile regression

In using multiple regression methods for prediction, one often considers the linear combination of explanatory variables as an index. Seeking a single such index when here are responses is rather more complicated. One classical approach to use coefficients from leading Canonical Correlation. However, based on variances unable disaggregate by quantile effects, lack robustness, and rely normal assumptions inference. An alternative canonical (CanRQ) seeks find that best predicts ?th response variables. Applying this “regression” generally, subsequent combinations chosen explain what earlier CanRQ components failed explain. While numerous technical issues need be addressed, major methodological issue concerns directionality: analysis requires notion larger or smaller well-defined. To address issue, sign at least coefficient will assumed non-negative. results can quite different those correlation, offer kind improvements offered quantiles in models.