fdcov (version 1.1.0)

ksample.perm: Multiple-sample permutation test for the equality of covariance operators of functional data

Description

The method performs a test for the equality of the covariance operators of multiple data samples. It can also perform all of the pairwise comparisons between the groups and compute a p-value for each of them. This feature is useful when the global null hypothesis is rejected, so one may want to find out which samples have different covariances.

Usage

ksample.perm(dat, grp, iter = 1000, perm = "sync", dist = "sq",
  adj = TRUE, comb = "tipp", part = FALSE, cent = FALSE, load = FALSE)

Arguments

dat

n X p data matrix of n samples of p long vectors.

grp

n long vector of group labels.

iter

Number of permutations. Defaults to 1000.

perm

Type of permutation, can be 'sync' (if all the data samples are of the same size) or 'pool'. Defaults to 'sync'

dist

Distance between covariance operators. Can be 'sq' (square-root distance), 'tr' (trace distance),'pr' (Procrustes distance), 'hs'(Hilbert-Schmidt distance) or 'op' (operator distance). Defaults to 'sq'.

adj

p-value adjustment. Defaults to TRUE.

comb

Can be 'tipp' (for Tippett), 'maxT', 'dire' (direct), 'fish' (Fisher) or 'lipt' (Liptak). Defaults to 'tipp'.

part

If FALSE, the function computes only the global p-value; otherwise it computes also all the p-values corresponding to the pairwise comparisons. Defaults to FALSE.

cent

If FALSE, the mean functions of the groups are supposed to be different, therefore data are centred before performing the test. Defaults to FALSE.

load

Boolean flag, which if TRUE, prints a loading bar.

Value

If part is set to FALSE, the output is the p-value associated to the global test. If part is TRUE, the function returns also all the p-values of the pairwise comparisons.

References

Cabassi, A., Pigoli, D., Secchi, P., Carter, P. A. (2017). Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology. Electron. J. Statist. 11(2), pp.3815--3840.

Pigoli, Davide, John A. D. Aston, Ian L. Dryden, and Piercesare Secchi (2014). "Distances and inference for covariance operators." Biometrika: 101(2):409<U+2013>422.

Examples

# NOT RUN {
## Phoneme data

library(fdcov)
library(fds)

# Create data set 
data(aa); data(ao); data(dcl);data(iy);data(sh)
dat = cbind(aa$y[,1:20],ao$y[,1:20],dcl$y[,1:20],iy$y[,1:20],sh$y[,1:20])
dat = t(dat)
grp = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20))

# Test the equality of the covariance operators
p = ksample.perm(dat, grp, iter=100, part = TRUE)
p$global # global p-value
p$partial # partial p-values
# }