Function to compute ranks from the dual (regression rankscore) process.
ranks(v, score="wilcoxon", tau=0.5, trim = NULL)The function returns two components. One is the ranks, the other is a scale factor which is the \(L_2\) norm of the score function. All score functions should be normalized to have mean zero.
object of class "rq.process" generated by rq()
The score function desired. Currently implemented score functions
are "wilcoxon", "normal", and "sign"
which are asymptotically optimal for
the logistic, Gaussian and Laplace location shift models respectively.
The "normal" score function is also sometimes called van der Waerden scores.
Also implemented are the "tau" which generalizes sign scores to an
arbitrary quantile, "interquartile" which is appropriate
for tests of scale shift, normalscale for Gaussian scale shift,
halfnormalscale for Gaussian scale shift only to the right of the median,
and lehmann for Lehmann local alternatives. See Koenker (2010) for
further details on the last three of these scores.
the optional value of tau if the "tau" score function is used.
optional trimming proportion parameter(s) -- only applicable for the
Wilcoxon score function -- when one value is provided there is symmetric
trimming of the score integral to the interval (trim, 1-trim), when
there are two values provided, then the trimming restricts the integration
to (trim[1], trim[2]).
See GJKP(1993) for further details.
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.
Koenker, R. Rank Tests for Heterogeneous Treatment Effects with Covariates, preprint.
rq, rq.test.rank anova
data(stackloss)
ranks(rq(stack.loss ~ stack.x, tau=-1))
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