summary.rq {quantreg}R Documentation

Summary method for Quantile Regression

Description

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)

Arguments

object This is an object of class "rq" produced by a call to rq().
se specifies the method used to compute standard 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 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.

References

Koenker, R. (2000) Quantile Regression.

See Also

rq

Examples

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=F),se="ker")
# default "br" alg, and compute kernel method se's