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In using multiple regression methods for prediction, one often considers thelinear combination of explanatory variables as an index. Seeking a single suchindex when here are multiple responses is rather more complicated. Oneclassical approach is to use the coefficients from the leading canonicalcorrelation. However, methods based on variances are unable to disaggregateresponses by quantile effects, lack robustness, and rely on normal assumptionsfor inference. We develop here an alternative regression quantile approach andapply it to an empirical study of the performance of large publicly heldcompanies and CEO compensation. The initial results are very promising.

Canonical Regression Quantiles with application to CEO compensation and predicting company performance