R: Linear Statistics with Expectation and Covariance

LinStatExpCov {libcoin} | R Documentation

## 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))

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

[Package libcoin version 1.0-5 Index]