# LinStatExpCov: Linear Statistics with Expectation and Covariance In libcoin: Linear Test Statistics for Permutation Inference

## Description

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

## Usage

 ```1 2 3 4 5``` ```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.

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

 ```1 2 3 4 5 6``` ```wilcox.test(Ozone ~ Month, data = airquality, subset = Month %in% c(5, 8)) aq <- subset(airquality, Month %in% c(5, 8)) X <- as.double(aq\$Month == 5) Y <- as.double(rank(aq\$Ozone)) doTest(LinStatExpCov(X, Y)) ```

libcoin documentation built on Aug. 22, 2020, 3:01 a.m.