Conduct an AMOC hypothesis test — amoc

Conduct an at-most one changepoint hypothesis test for changes in the covariance operator of functional data based on the FKWC (functional Kruskal–Wallis covariance changepoint) procedures outlined by Ramsay and Chenouri (2025).

Usage

amoc_test(data, ranks = NULL, depth = c("RPD", "FM", "LTR", "FMd", "RPDd"))

Arguments

data: Data in matrix or data.frame form, where each row is an observation and each column is a dimension.
ranks: Optional if data is already ranked.
depth: Depth function of choice.

Value

A list consisting of:

$changepoint : Index of the estimated changepoint.
$pvalue : The p-value based on the null distribution.
$method : A string "AMOC test (KWCChangepoint)"

Note

The options for the depth argument are as follows:

RPD: Random projection depth
FM: Frainman-Muniz depth
LTR: $L^2$-root depth, most suitable for detecting changes in the norm
FMd: Frainman-Muniz depth of the data and its first order derivative
RPDd: Random projection depth of the data and its first order derivative

The depth arguments that incorporate the first order derivative (which is approximated using fda.usc::fdata.deriv) result in a more robust detection of changes in the covariance structure (Ramsay and Chenouri, 2025).

References

Ramsay, K., & Chenouri, S. (2025). Robust changepoint detection in the variability of multivariate functional data. Journal of Nonparametric Statistics. https://doi.org/10.1080/10485252.2025.2503891

Examples

set.seed(11)
test_data <- rbind(replicate(3,rnorm(200,1,1)), #before changepoint
                   replicate(3,rnorm(200,1,5))) #after changepoint

amoc_test(test_data)
#> $changepoint
#> [1] 200
#> 
#> $pvalue
#> [1] 0
#> 
#> $method
#> [1] "AMOC test (KWCChangepoint)"
#>