summary.rq {quantreg}  R Documentation 
Returns a summary list for a quantile regression fit. A null value will be returned if printing is invoked.
summary.rq(object, se="nid", covariance=TRUE, hs = TRUE, ...) summary.rqs(object, ...)
object 
This is an object of class "rq" or "rqs" produced by
a call to rq() , depending on whether one or more taus are
specified.

se 
specifies the method used to compute standard standard errors. There
are currently five available methods:

covariance 
logical flag to indicate whether the full covariance matrix of the estimated parameters should be returned. 
hs 
Use Hall Sheather bandwidth for sparsity estimation If false revert to Bofinger bandwidth. 
... 
Optional arguments to summary, e.g. bsmethod to use bootstrapping.
see boot.rq

When the default summary method is used, it tries to estimate a sandwich form of the asymptotic covariance matrix and this involves estimating the conditional density at each of the sample observations, negative estimates can occur if there is crossing of the neighboring quantile surfaces used to compute the difference quotient estimate. If the number of these is large relative to the sample size it is sometimes an indication that some additional nonlinearity in the covariates would be helpful, for instance quadratic effects.
a list is returned with the following components, when object
is of class "rqs"
then there is a list of such lists.
coefficients 
a p by 4 matrix consisting of the coefficients, their estimated standard errors, their tstatistics, and their associated pvalues. 
cov 
the estimated covariance matrix for the coefficients in the model,
provided that cov=TRUE in the called sequence.

Hinv 
inverse of the estimated Hessian matrix returned if cov=TRUE and
se != "iid" .

J 
Outer product of gradient matrix returned if cov=TRUE and se
!= "iid" . The Huber sandwich is cov = Hinv %*% J %*% Hinv .

Koenker, R. (2004) Quantile Regression.
data(stackloss) y < stack.loss x < stack.x summary(rq(y ~ x, method="fn")) # Compute se's for fit using "nid" method. summary(rq(y ~ x, ci=FALSE),se="ker") # default "br" alg, and compute kernel method se's