<!doctype s-function-doc system "s-function-doc.dtd" [
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<s-function-doc>
<s-topics>
<s-topic>rrs.test</s-topic>
</s-topics>
<s-title>
Quantile Regression Rankscore Test
</s-title>
<s-description>
Function to compute regression rankscore test of a linear hypothesis
based on the dual quantile regression process.  A test of  the 
hypothesis, 
is carried out by estimating the restricted model and constructing
a test based on the dual process under the restricted model.  The
details of the test are described in GJKP(1993).  The test has a
Rao-score, Lagrange-multiplier interpretation since in effect it
is based on the value of the gradient of unrestricted quantile regression
problem evaluated under the null.  This function will eventually be
superseded by a more general anova() method for rq.
</s-description>
<s-usage>
<s-old-style-usage>
rrs.test(x0, x1, y, v, score="wilcoxon")
</s-old-style-usage>
</s-usage>
<s-args-required>
<s-arg name= x0 >
the matrix of maintained regressors, a column of ones is appended automatically.
</s-arg>
<s-arg name= x1 >
matrix of covariates under test.
</s-arg>
</s-args-required>
<s-args-optional>
<s-arg name= y >
response variable, may be omitted if v is provided.
</s-arg>
<s-arg name= v >
object of class rq.process generated e.g. by rq(y~x0,tau=-1)
</s-arg>
<s-arg name= score >
Score function for test (see rq.ranks())
</s-arg>
</s-args-optional>
<s-value>
Test statistic sn is asymptotically Chi-squared with rank(X1) dfs.
The vector of ranks is also returned as component rank.
</s-value>
<s-details>
See GJKP(1993)
</s-details>
<s-section name = "REFERENCES">
       [1] Gutenbrunner,  C.,  J.  Jureckova,   Koenker,  R.  and
       Portnoy,  S.(1993)  "Tests  of Linear Hypotheses  based on
       Regression  Rank   Scores",   Journal   of   Nonparametric
       Statistics, (2), 307-331.
<br><br>

       [2] Koenker, R.W. and d'Orey (1994).  "Remark on  Alg.  AS
       229:  Computing  Dual  Regression Quantiles and Regression
       Rank Scores", Applied Statistics, 43, 410-414.
</s-section>
<s-see>
rq, rq.ranks
</s-see>
<s-examples>
<s-example>
# Test that covariates 2 and 3 belong in stackloss model using Wilcoxon scores.
rrs.test(stack.x[,1],stack.x[,2:3],stack.loss)
</s-example>
</s-examples>
<s-keywords>
<s-keyword>librobust</s-keyword>
<s-keyword>regression</s-keyword>
</s-keywords>
<s-docclass>
function
</s-docclass>
</s-function-doc>
