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 This function will eventually be superseded by a more general anova() method for rq.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)