Quantile Regression Rankscore Test
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superseded by a more general anova() method for rq.
USAGE:
rrs.test(x0, x1, y, v, score="wilcoxon")
REQUIRED ARGUMENTS:
- x0
-
the matrix of maintained regressors, a column of ones is appended automatically.
- x1
-
matrix of covariates under test.
OPTIONAL ARGUMENTS:
- y
-
response variable, may be omitted if v is provided.
- v
-
object of class rq.process generated e.g. by rq(y~x0,tau=-1)
- score
-
Score function for test (see rq.ranks())
VALUE:
Test statistic sn is asymptotically Chi-squared with rank(X1) dfs.
The vector of ranks is also returned as component rank.
DETAILS:
See GJKP(1993)
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.
[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.
SEE ALSO:
rq, rq.ranks
EXAMPLES:
# Test that covariates 2 and 3 belong in stackloss model using Wilcoxon scores.
rrs.test(stack.x[,1],stack.x[,2:3],stack.loss)