Q:

Goodness of fit tests for quantile regression in R

What goodness of fit tests are usually used for quantile regression?  Ideally I need something similar to F-test in linear regression, but something like AIC in logistic regression will suite as well.  I use quantreg R package, but found only some Khmaladze test in there.  To be fair I hardly understand what is does. 

A:

quantreg includes several AIC functions: "AIC.nlrq", "AIC.rq", "AIC.rqs" and "AIC.rqss" and similar log likelihood functions.  
It also has a vignette at vignette("rq",package="quantreg"). 
Do these do what you want? 