quantreg (version 4.77)

summary.rqss: Summary of rqss fit

Description

Summary Method for a fitted rqss model.

Usage

## S3 method for class 'rqss':
summary(object, cov = FALSE, ztol = 1e-5, ...)

Arguments

object

an object returned from rqss fitting, describing an additive model estimating a conditional quantile function. See qss for details on how to specify these terms.

cov

if TRUE return covariance matrix for the parametric components as Vcov and a list of covariance matrices for the nonparametric components as Vqss

ztol

Zero tolerance parameter used to determine the number of zero residuals indicating the estimated parametric dimension of the model, the so-called effective degrees of freedom.

...

additional arguments

Value

• coef
  Table of estimated coefficients and their standard errors, t-statistics, and p-values for the parametric components of the model
• qsstab
  Table of approximate F statistics, effective degrees of freedom and values of the penalty terms for each of the additive nonparametric components of the model, and the lambda values assigned to each.
• fidelity
  Value of the quantile regression objective function.
• tau
  Quantile of the estimated model
• formula
  formula of the estimated model
• edf
  Effective degrees of freedom of the fitted model, defined as the number of zero residuals of the fitted model, see Koenker Mizera (2003) for details.
• n
  The sample size used to fit the model.
• Vcov
  Estimated covariance matrix of the fitted parametric component
• Vqss
  List of estimated covariance matrices of the fitted nonparametric component

Details

This is a highly experimental function intended to explore inferential methods for rqss fitting. The function is modeled after summary.gam in Simon Wood's (2006) mgcv package. (Of course, Simon should not be blamed for any deficiencies in the current implementation. The basic idea is to condition on the lambda selection and construct quasi-Bayesian credibility intervals based on normal approximation of the "posterior," as computed using the Powell kernel estimate of the usual quantile regression sandwich. See summary.rq for further details and references. The function produces a conventional coefficient table with standard errors t-statistics and p-values for the coefficients on the parametric part of the model, and another table for additive nonparametric effects. The latter reports F statistics intended to evaluate the significance of these components individually. In addition the fidelity (value of the QR objective function evaluated at the fitted model), the effective degrees of freedom, and the sample size are reported.

References

[1] Koenker, R., P. Ng and S. Portnoy, (1994) Quantile Smoothing Splines; Biometrika 81, 673--680.

[2] Koenker, R. and I. Mizera, (2003) Penalized Triograms: Total Variation Regularization for Bivariate Smoothing; JRSS(B) 66, 145--163.

[3] Wood, S. (2006) Generalized Additive Models, Chapman-Hall.

See Also

plot.rqss

Examples

n <- 200
x <- sort(rchisq(n,4))
z <- x + rnorm(n)
y <- log(x)+ .1*(log(x))^2 + log(x)*rnorm(n)/4 + z
f  <- rqss(y ~ qss(x) + z)
summary(f)