quantreg (version 4.77)

rqss.object: RQSS Objects and Summarization Thereof

Description

Functions to reveal the inner meaning of objects created by rqss fitting.

Usage

## S3 method for class 'rqss':
logLik(object, ...)
## S3 method for class 'rqss':
AIC(object, ..., k=2)
## S3 method for class 'rqss':
print(x, ...)
## S3 method for class 'rqss':
resid(object, ...)
## S3 method for class 'rqss':
fitted(object, ...)

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.

x

an rqss object, as above.

k

a constant factor governing the weight attached to the penalty term on effective degrees of freedom of the fit. By default k =2 corresponding to the Akaike version of the penalty, negative values indicate that the k should be set to log(n) as propose

...

additional arguments

Value

• The function summary.rqss returns a list consisting of the following components:
• fidelity
  Value of the quantile regression objective function.
• penalty
  A list consisting of the values of the total variation smoothing penalty for each of additive components.
• edf
  Effective degrees of freedom of the fitted model, defined as the number of zero residuals of the fitted model, Koenker Mizera (2003) for details.
• qssedfs
  A list of effective degrees of freedom for each of the additive components of the fitted model, defined as the number of non-zero elements of each penalty component of the residual vector.
• lamdas
  A list of the lambdas specified for each of the additive components of the model.

Details

Total variation regularization for univariate and bivariate nonparametric quantile smoothing is described in Koenker, Ng and Portnoy (1994) and Koenker and Mizera(2003) respectively. The additive model extension of this approach depends crucially on the sparse linear algebra implementation for R described in Koenker and Ng (2003). Eventually, these functions should be expanded to provide an automated lambda selection procedure.

References

[1] Koenker, R. and S. Portnoy (1997) The Gaussian Hare and the Laplacean Tortoise: Computability of Squared-error vs Absolute Error Estimators, (with discussion). Statistical Science 12, 279--300.

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

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

[4] Koenker, R. and P. Ng (2003) SparseM: A Sparse Linear Algebra Package for R, J. Stat. Software.

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
plot(x, y-z)
f.N  <- rqss(y ~ qss(x, constraint= "N") + z)
f.I  <- rqss(y ~ qss(x, constraint= "I") + z)
f.CI <- rqss(y ~ qss(x, constraint= "CI") + z)

lines(x[-1], f.N $coef[1] + f.N $coef[-(1:2)])
lines(x[-1], f.I $coef[1] + f.I $coef[-(1:2)], col="blue")
lines(x[-1], f.CI$coef[1] + f.CI$coef[-(1:2)], col="red")

## A bivariate example
data(CobarOre)
fCO <- rqss(z ~ qss(cbind(x,y), lambda= .08), data=CobarOre)
plot(fCO)