rq.test.khmal: Estimates Quantile Regression Model and Test Statistics

Description

Estimates a model and produces the output necessary to test the location and location-scale shift hypotheses. Returns an object of the class "khmal".

Usage

rq.test.khmal( formula, data, taus=seq(0.2,0.8,by=0.002), 
location.scale = TRUE,  trim = c(0.25, 0.75) )

Arguments

formula

a symbolic description of the model to be fit. The details of model specification are given below.

data

dataframe containing the regressand and regressors. It should not contain a column of ones.

taus

vector of quantiles to be estimated. Default range is 0.2 to 0.8, increasing by 0.002 units.

location.scale

a logic value indicating whether the location-scale shift hypothesis (default) or the location shift hypothesis (F) should be tested.

trim

a vector indicating the lower and upper bound of the quantiles to included in the computation of the test statistics (only, not estimates). This might be required due to tail behavior.

Value

a R structure is returned
formulaa symbolic description of the fitted model.
tausvector with estimated quantiles.
Jn$X'X$ of least squares.
fitEstimated coefficients for all quantiles.
HfitArray with inverse quantile regression covariance matrices.
varsVariables names, useful for plotting functions.
var.listNumerical list of variables to be plotted. By default all variables are plotted. A restricted set of variables can be specified by providing a numerical vector indicating the desired variables. The convention is that 1 corresponds to the intercept, 2 to the first independent variable entered in "formula" and so on. See example for further details.
location.scalea logic value indicating whether the location-scale shift hypothesis (default) or the location shift hypothesis (F) was performed.
bMatrix with the coefficients from the least-squares regression of the estimated quantile regression slopes on the intercept.
JOutput of standardize().
VtildeOutput of khmaladzize() for the joint hypothesis testing.
vtildeOutput of khmaladzize() for the individual hypotheses testing.
Tvtildevtilde appropriately transformed to compute the individual test statistics of the location-scale shift hypothesis.
trima vector indicating the lower and upper bound of the quantiles included in the computation of the test statistics (only, not estimates).
KnJoint location-scale shift test statistic. Only returned if location.scale is TRUE.
KHnIndividual location-scale shift test statistics. Only returned if location.scale is TRUE.
TnJoint location shift test statistic. Only returned if location.scale is FALSE.
THnIndividual location shift test statistics. Only returned if location.scale is FALSE.

References

Koenker, Roger and Zhijie Xiao (2000), "Inference on the Quantile Regression Process'', unpublished. http://www.econ.uiuc.edu/~roger/research/inference/inference.html

Examples

Run this code

data(barro)
fit.Lonly <- rq.test.khmal( y.net ~ lgdp2 + fse2 + gedy2 + Iy2 + gcony2, 
data = barro, location.scale = FALSE )

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