Title:	Linear Test Statistics for Permutation Inference
Date:	2026-03-06
Version:	1.0-11
Description:	Basic infrastructure for linear test statistics and permutation inference in the framework of Strasser and Weber (1999) https://epub.wu.ac.at/102/. This package must not be used by end-users. CRAN package 'coin' implements all user interfaces and is ready to be used by anyone.
Depends:	R (≥ 3.4.0)
Suggests:	coin, bibtex
Imports:	stats, mvtnorm
LinkingTo:	mvtnorm
NeedsCompilation:	yes
License:	GPL-2
Packaged:	2026-03-06 15:32:01 UTC; rchecker
Author:	Torsten Hothorn [aut, cre], Henric Winell [aut]
Maintainer:	Torsten Hothorn <Torsten.Hothorn@R-project.org>
Repository:	CRAN
Date/Publication:	2026-03-06 17:40:10 UTC

Linear Statistics with Expectation and Covariance

Description

Strasser-Weber type linear statistics and their expectation and covariance under the independence hypothesis

Usage

LinStatExpCov(X, Y, ix = NULL, iy = NULL, weights = integer(0),
              subset = integer(0), block = integer(0), checkNAs = TRUE,
              varonly = FALSE, nresample = 0, standardise = FALSE,
              tol = sqrt(.Machine$double.eps))
lmult(x, object)

Arguments

Details

This function implements the permutation test framework by Strasser and Weber (1999), see also Hothorn, Hornik, van de Wiel, and Zeileis (2006) and Hothorn, Hornik, van de Wiel, and Zeileis (2008).

The function, after minimal preprocessing, calls the underlying C code and computes the linear statistic, its expectation and covariance and, optionally, nresample samples from its permutation distribution.

When both ix and iy are missing, the number of rows of X and Y is the same, ie the number of observations.

When X is missing and ix a factor, the code proceeds as if X were a dummy matrix of ix without explicitly computing this matrix.

Both ix and iy being present means the code treats them as subsetting vectors for X and Y. Note that ix = 0 or iy = 0 means that the corresponding observation is missing and the first row or X and Y must be zero.

lmult allows left-multiplication of a contrast matrix when X was (equivalent to) a factor.

Value

A list.

References

Hothorn T., Hornik K., van de Wiel M. A., Zeileis A. (2006). “A Lego System for Conditional Inference.” The American Statistician, 60(3), 257–263. doi:10.1198/000313006X118430.

Hothorn T., Hornik K., van de Wiel M. A., Zeileis A. (2008). “Implementing a Class of Permutation Tests: The coin Package.” Journal of Statistical Software, 28(8), 1–23. doi:10.18637/jss.v028.i08.

Strasser H., Weber C. (1999). “On the Asymptotic Theory of Permutation Statistics.” Mathematical Methods of Statistics, 8, 220-250. Preprint available from https://epub.wu.ac.at/102.

Examples

wilcox.test(Ozone ~ Month, data = airquality, subset = Month %in% c(5, 8),
            exact = FALSE, correct = FALSE)

aq <- subset(airquality, Month %in% c(5, 8))
X <- as.double(aq$Month == 5)
Y <- as.double(rank(aq$Ozone, na.last = "keep"))
doTest(LinStatExpCov(X, Y))

Cross Tabulation

Description

Efficient weighted cross tabulation of two factors and a block

Usage

ctabs(ix, iy = integer(0), block = integer(0), weights = integer(0),
      subset = integer(0), checkNAs = TRUE)

Arguments

Details

A faster version of xtabs(weights ~ ix + iy + block, subset).

Value

If block is present, a three-way table. Otherwise, a one- or two-dimensional table.

Examples

ctabs(ix = 1:5, iy = 1:5, weights = 1:5 / 5)

Permutation Test

Description

Perform permutation test for a linear statistic

Usage

doTest(object, teststat = c("maximum", "quadratic", "scalar"),
       alternative = c("two.sided", "less", "greater"), pvalue = TRUE,
       lower = FALSE, log = FALSE, PermutedStatistics = FALSE,
       minbucket = 10L, ordered = TRUE, maxselect = object$Xfactor,
       pargs = GenzBretz())

Arguments

Details

Computes a test statistic, a corresponding p-value and, optionally, cutpoints for maximally selected statistics.

Value

A list.