group.action {RATest}

General Construction of Permutation Tests: Group Actions

Description

Calculates the pre-specified actions on data. Consider data Z taking values in a sample space \Omega. Let \mathbf{G} be a finite group of transformations from \Omega onto itself, with M=\vert \mathbf{G}\vert. This function applies gZ as g varies in \bf{G}. If Z is a vector of sizeN and the actions g are permutations, M=N!. If the actions g are sign changes, then M=\{1,-1\}^{N}.

Usage

group.action(Z, M, type = "permutations")

Arguments

Z

Numeric. A vector of size N to which the group action will act on. In the two-sample testing problem, Z is the pooled sample.

M

Numeric. Number of actions to be performed. This is the number of transformations used in the stochastic approximation to the test. This is due to the fact that in some cases M=\vert \mathbf{G}\vert is too large, which makes the application of the actions computationally expensive.

type

Character. The action to be performed. It represents gx, the action the action of g\in\mathbf{G} on x\in\Omega. It can be either permutations or sign changes.

Value

Numeric. A matrix of size N\times M where N is the size of input Z and M is the number of actions to be performed on Z.

Author(s)

Maurcio Olivares

Ignacio Sarmiento Barbieri

References

Lehmann, Erich L. and Romano, Joseph P (2005) Testing statistical hypotheses.Springer Science & Business Media.