# rqss.object

##### RQSS Objects and Summarization Thereof

Functions to reveal the inner meaning of objects created by `rqss`

fitting.

- Keywords
- robust, regression, smooth

##### Usage

```
# S3 method for rqss
logLik(object, ...)
# S3 method for rqss
AIC(object, ..., k=2)
# S3 method for rqss
print(x, ...)
# S3 method for rqss
resid(object, ...)
# S3 method for 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 proposed by Schwarz (1978).

- ...
additional arguments

##### 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.

##### Value

The function `summary.rqss`

returns a list consisting of
the following components:

Value of the quantile regression objective function.

A list consisting of the values of the total variation smoothing penalty for each of additive components.

Effective degrees of freedom of the fitted model, defined as the number of zero residuals of the fitted model, Koenker Mizera (2003) for details.

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.

A list of the lambdas specified for each of the additive components of the model.

##### 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

##### Examples

```
# NOT RUN {
require(MatrixModels)
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)
# }
```

*Documentation reproduced from package quantreg, version 5.54, License: GPL (>= 2)*