In quantile regression, the goal is to estimate theγ quantile of Y given values for p predictors. Methods for making inferences about the individual slope parameters have been proposed, some of which have been found to perform very well in simulations. But for an omnibus test that all slope parameters are zero, it appears that little is known about how best to proceed. For the special case γ =.5, a drop-in-dispersion test has been recommended, but it requires a large sample size to control the probability of a Type I error and it assumes that the usual error term is homoscedastic. The article suggests an alternative method that performs well in simulations, it allows heteroscedasticity, and it can be used when γ ≠ .5.
Wilcox, Rand R.
"An Omnibus Test When Using a Regression Estimator With Multiple Predictors,"
Journal of Modern Applied Statistical Methods:
2, Article 3.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss2/3