Stefan:  Your comparison of two models, one with a nested reduced set of 
parameters by fixing the others at zero, with anova() can be used to make 
inference either based on a likelihood ratio form of test or the rankscore 
test for a given quantile (see ?anova.rq and the vignette for literature 
citations with details on the test statistics).   So this comparison 
corresponds to the typical linear model hypothesis of a set of parameters 
equaling zero.  I prefer the rankscore test if sample sizes are not too 
large (e.g., <5,000). 

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  brian_cade@usgs.gov
tel:  970 226-9326



From:
stefan23 <stefan.voigt@uni-konstanz.de>
To:
r-help@r-project.org
Date:
07/28/2012 10:32 PM
Subject:
[R] quantreg Wald-Test
Sent by:
r-help-bounces@r-project.org



Dear all,
I know that my question is somewhat special but I tried several times to
solve the problems on my own but I am unfortunately not able to compute 
the
following test statistic using the quantreg package. Well, here we go, I
appreciate every little comment or help as I really do not know how to 
tell
R what I want it to do^^
My situation is as follows: I have a data set containing a (dependent)
vector Y and the regressor X. My aim is to check whether the two variables
do not granger-cause each other in quantiles. I started to compute via
quantreg for a single tau:= q:
rq(Y_t~Y_(t-1)+Y_(t-2)+...+X_(t-1)+X_(t-2)+...,tau=q) 
This gives me the quantile regression coefficients. Now I want to check
whether all the coefficients of X are equal to zero (for this specific 
tau).
Can I do this by applying rq.anova ? I have already asked a similiar
question but I am not sure if anova is really calculating this for me..
Currently I am calculating
fitunrestricted=rq(Y_t~Y_(t-1)+Y_(t-2)+...+X_(t-1)+X_(t-2)+...,tau=q) 
fitrestrited=rq(Y_t~Y_(t-1)+Y_(t-2)+...,tau=q)
anova(fitrestricted,fitunrestricted)
If this is correct can you tell me how the test value is calculated in 
this
case, or in other words:
My next step is going to replicate this procedure for a whole range of
quantiles (say for tau in [a,b]). To apply a sup-Wald-test I am wondering 
if
it is correct to choose the maximum of the different test values and to
simulate the critical values by using the data tabulated in Andrees(1993)
(or simulate the vectors of independent Brownian Motions)...please feel 
free
to comment, I am really looking forward to your help!
Thank you very much 
Cheers
Stefan




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