Goodness of fit and related inference processes for quantile regression

We introduce a goodness-of-fit process for quantile regression analogous to the conventional R-2 statistic of least squares regression. Several relate d inference processes designed to test composite hypotheses about the combi ned effect of several covariates over an entire range of conditional quanti le functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier p-sample goodness-of-fi t theory involving Bessel processes. The approach is illustrated with some hypothetical examples, an application to recent empirical models of interna tional economic growth, and some Monte Carlo evidence.