quantreg (version 4.77)

summary.rq: Summary methods for Quantile Regression

Description

Returns a summary list for a quantile regression fit. A null value will be returned if printing is invoked.

Usage

## S3 method for class 'rq':
summary(object, se = NULL, covariance=FALSE, hs = TRUE,  ...)
## S3 method for class 'rqs':
summary(object, ...)

Arguments

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:

1. "rank"which produces confidence intervals for the estimated parameters by inverting a rank test as described 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, 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 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 %in% c("nid","ker"), note that for se = "boot" there is no way to split the estimated covariance matrix into its sandwich constituent parts.
• J
  Unscaled Outer product of gradient matrix returned if cov=TRUE and se != "iid". The Huber sandwich is cov = tau (1-tau) Hinv %*% J %*% Hinv. as for the Hinv component, there is no J component when se == "boot". (Note that to make the Huber sandwich you need to add the tau (1-tau) mayonnaise yourself.)

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. A warning message is issued when such negative estimates exist indicating the number of occurrences -- if this number constitutes a large proportion of the sample size, then it would be prudent to consider an alternative inference method like the bootstrap. 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. Note that the default se method is rank, unless the sample size exceeds 1001, in which case the rank method is used.

References

Koenker, R. (2004) Quantile Regression.

Bilias, Y. Chen, S. and Z. Ying, Simple resampling methods for censored quantile regression, J. of Econometrics, 99, 373-386.

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