Let (<italic>X</italic><sub>1</sub>, <italic>Y</italic><sub>1</sub>), …, (<italic>X</italic>, <italic>Y</italic>) be independent and identically distributed random variables and let <italic>l</italic>(<italic>x</italic>) be the unknown <italic>p</italic>-quantile regression curve of <italic>Y</italic> conditional on <italic>X</italic>. A quantile smoother <italic>l</italic>(<italic>x</italic>) is a localized, nonlinear estimator of <italic>l</italic>(<italic>x</italic>). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {<italic>l</italic>(<italic>x</italic>) – <italic>l</italic>(<italic>x</italic>)}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup<sub>0≤</sub> |<italic>l</italic>(<italic>x</italic>) − <italic>l</italic>(<italic>x</italic>)|. The derived result helps in the construction of a uniform confidence band for the quantile curve <italic>l</italic>(<italic>x</italic>). This confidence band can be applied as a econometric model check. An economic application considers the relation between age and earnings in the labor market by means of parametric model specification tests, which presents a new framework to describe trends in the entire wage distribution in a parsimonious way.
