Conditional quantile identification ($M(\theta )>M({\theta }_0)(\theta \ne {\theta }_0)$)

If the conditional error distribution function is continuous and strictly increasing with $\tau$-quantile zero, the conditional expected check loss is uniquely minimized at zero fitted displacement. If every incorrect parameter differs from the true regression function on an event of positive probability, averaging these nonnegative conditional risk differences gives strict identifiability of the true parameter. Integrable errors and bounded regression functions supply finite risks.