khmaladze.test {quantreg}  R Documentation 
Tests of the hypothesis that a linear model specification is of the location and locationscale shift form. The tests are based on the DoobMeyer transformation approach proposed by Khmaladze(1981) for general goodness of fit problems, and adapted to quantile regression by Koenker and Xiao (2001).
khmaladze.test( fit, nullH = "locationscale" , trim = c(0.25, 0.75) )
fit 
an object produced by rqProcess containing
components describing the quantile regression process for
the model.

nullH 
a character vector indicating whether the "locationscale" shift hypothesis (default) or the "location" shift hypothesis should be tested. 
trim 
a vector indicating the lower and upper bound of the quantiles to included in the computation of the test statistics (only, not estimates). This might be required due to tail behavior. 
an object of class khmaladze is returned containing:
nullH 
The form of the null hypothesis. 
Tn 
Joint test statistic of the hypothesis that all the slope parameters of the model satisfy the hypothesis. 
THn 
Vector of test statistics testing whether individual slope parameters satisfy the null hypothesis. 
Khmaladze, E. (1981) ``Martingale Approach in the Theory of Goodnessoffit Tests,'' textit{Theory of Prob. and its Apps}, 26, 240–257.
Koenker, Roger and Zhijie Xiao (2000), "Inference on the Quantile Regression Process'', textit{Econometrica}, 81, 1583–1612. http://www.econ.uiuc.edu/~roger/research/inference/inference.html
data(barro) fit < rqProcess( y.net ~ lgdp2 + fse2 + gedy2 + Iy2 + gcony2, data = barro, taus = seq(.1,.9,by = .05)) khmaladze.test(fit, nullH = "location")