Qtools (version 1.5.8)

sparsity.rqt: Sparsity Estimation

Description

This function estimates the density and sparsity functions of the residuals from a rq or a rqt object.

Usage

sparsity(object, se = "nid", hs = TRUE)
# S3 method for rq
sparsity(object, se = "nid", hs = TRUE)
# S3 method for rqs
sparsity(object, se = "nid", hs = TRUE)
# S3 method for rqt
sparsity(object, se = "nid", hs = TRUE)

Value

sparsity returns an object of class

list that contains three elements:

density

estimate of the density of the residuals.

sparsity

estimate of the sparsity of the residuals.

bandwidth

bandwidth used for estimation.

Arguments

object

a rq, rqs or rqt object.

se

"iid" if errors are assumed independent and identically distributed; "nid" (default) if independent but not identically distributed; "ker" which uses a kernel estimate of the sandwich as proposed by Powell (1991).

hs

logical flag. If TRUE (default) the Hall-Sheather rule is used. Otherwise, the Bofinger's rule is used.

Author

Marco Geraci

Details

This function is based on the code from quantreg::summary.rq and quantreg::bandwidth.rq to estimate the sparsity function for linear quantile regression models (Koenker and Bassett, 1978) and transformation models of Geraci and Jones (2014).

References

Geraci M and Jones MC. Improved transformation-based quantile regression. Canadian Journal of Statistics 2015;43(1):118-132.

Koenker R. quantreg: Quantile Regression. 2016. R package version 5.29.

Koenker R, Bassett G. Regression quantiles. Econometrica. 1978;46(1):33-50.

Powell JL. Estimation of monotonic regression models under quantile restrictions. In: Barnett W, Powell J, Tauchen G, editors. Nonparametric and Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium on Economic Theory and Econometrics. New York, NY: Cambridge University Press 1991. p. 357-84.

See Also

rq

Examples

if (FALSE) {

data(trees)

# 'rqt' object

fit.rqt <- tsrq(Volume ~ Height, tsf = "bc", symm = FALSE, data = trees,
	lambda = seq(-10, 10, by = 0.01), tau = 0.5)
sparsity(fit.rqt)

# 'rq' object

fit.rq <- rq(Volume ~ Height, data = trees)
sparsity(fit.rq, se = "iid")
sparsity(fit.rq, se = "nid")
sparsity(fit.rq, se = "ker")
}