quantreg (version 3.34)

summary.rq: 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=TRUE, hs = TRUE,  ...)

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 i

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

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=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.

Details

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.

References

Koenker, R. (2004) Quantile Regression.

See Also

rq bandwidth.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=FALSE),se="ker")
# default "br" alg, and compute kernel method se's