Quantile Regression: On Inferences about the Slopes Corresponding to One, Two or Three Quantiles

Abstract

The problem of testing hypotheses about the slope of a quantile regression line when the sample size is small is considered. A modified bootstrap method is suggested that is found to have certain advantages over the inverse rank method recommended by Koenker (1994). A method is suggested that simultaneously controls the probability of at least one Type I error when performing two or three tests corresponding to two or three specific quantiles. Using data from actual studies, it is illustrated that the new method can yield substantially shorter confidence intervals than the rank inverse method and, even with a large sample size, the choice of method can matter.