LinStatExpCov: Linear Statistics with Expectation and Covariance

In libcoin: Linear Test Statistics for Permutation Inference

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

X	numeric matrix of transformations.
Y	numeric matrix of influence functions.
ix	an optional integer vector expanding X.
iy	an optional integer vector expanding Y.
weights	an optional integer vector of non-negative case weights.
subset	an optional integer vector defining a subset of observations.
block	an optional factor defining independent blocks of observations.
checkNAs	a logical for switching off missing value checks. This included switching off checks for suitable values of subset. Use at your own risk.
varonly	a logical asking for variances only.
nresample	an integer defining the number of permuted statistics to draw.
standardise	a logical asking to standardise the permuted statistics.
tol	tolerance for zero variances.
x	a contrast matrix to be left-multiplied in case X was a factor.
object	an object of class "LinStatExpCov".

Details

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

Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics 8(2), 220–250.

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))

libcoin documentation built on Sept. 27, 2023, 5:08 p.m.