Returns a summary list for a quantile regression fit. A null value
will be returned if printing is invoked.
USAGE:
summary.rq(object, se="nid", covariance=T)
REQUIRED ARGUMENTS:
object
This is an object of class rq produced by a call to rq().
OPTIONAL ARGUMENTS:
se
specifies the method used to compute standard errors. There
are currently three available methods:
1. "iid" which presumes that the errors are iid and computes
an estimate of the asymptotic covariance matrix as in KB(1978).
2. "nid" which presumes local (in tau) linearity (in x) of
the conditional quantile functions and computes a Huber
sandwich estimate using a local estimate of the sparsity.
3. "ker" which uses a kernel estimate of the sandwich as proposed
by Powell(1990).
covariance
logical flag to indicate whether the full covariance matrix of the
estimated parameters should be returned.
VALUE:
a list is returned with the following components
coefficients
a p by 4 matrix consisting of the coefficients, their estimated standard
errors, their t-statistics, and their associated p-values.
cov
the estimated covariance matrix for the coefficients in the model,
provided that cov=T in the called sequence.
Hinv
inverse of the estimated Hessian matrix returned if cov=T and se!=iid.
J
Outer product of gradient matrix returned if cov=T and se!=iid.
The Huber sandwich is cov = Hinv%*%J%*%Hinv.
SIDE EFFECTS:
DETAILS:
REFERENCES:
Koenker, R. (2000) Quantile Regression.
SEE ALSO:
.
EXAMPLES:
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=F),se="ker") #default "br" alg, and compute kernel method se's
librobust
regression