  In the present paper we investigate the predictive risk of possibly
misspecified quantile regression functions. The in-sample risk is well-known to
be an overly optimistic estimate of the predictive risk and we provide two
relatively simple (asymptotic) characterizations of the associated bias, also
called expected optimism. We propose estimates for the expected optimism and
the predictive risk, and establish their uniform consistency under mild
conditions. Our results hold for models of moderately growing size and allow
the quantile function to be incorrectly specified. Empirical evidence from our
estimates is encouraging as it compares favorably with cross-validation.
