Multisample hypothesis test for difference in covariance operators

Executes a multisample hypothesis test for differences in covariance operators using functional Kruskal–Wallis tests for covariance (FKWC) as outlined by Ramsay and Chenouri (2024). The function requires the first order derivative of the functional data in order to better detect changes.

Usage

fkwc_multisample(data, derivs, g, p = 20)

Arguments

data

Functional data in matrix or data.frame form, where each row is an observation/function and the columns are the grid.

derivs

First order derivative of the functional data in matrix or data.frame form.

g

A factor object that indicates which sample each row of data belongs to.

p

Number of random projections to be generated in order to compute random projection depths of the data.

Value

A list consisting of:

• $statistic : The observed test statistic.

• $pvalue : The p-value based on the null distribution.

• $method : A string "FKWC"

References

Ramsay, K., & Chenouri, S. (2024). Robust nonparametric hypothesis tests for differences in the covariance structure of functional data. Canadian Journal of Statistics, 52 (1), 43–78. https://doi.org/10.1002/cjs.11767

See also

fda.usc::fdata.deriv(): for approximating the first order derivative if unavailable.

fkwc_posthoc(): for a post-hoc version of this test

Examples

set.seed(111)
t <- seq(0, 1, length.out = 200)

### Generating three sets of Brownian curves with different kernels, each
### kernel generating 20 observations
# Brownian process 1
fd1 <- fda.usc::rproc2fdata(n = 20, t = t, sigma = "brownian",
                           par.list = list(scale = 10, theta = 1))
fd1_d <- fda.usc::fdata.deriv(fd1)

# Brownian process 2
fd2 <- fda.usc::rproc2fdata(n = 20, t = t, sigma = "brownian",
                           par.list = list(scale = 1, theta = 1))
fd2_d <- fda.usc::fdata.deriv(fd2)

# Brownian process 3
fd3 <- fda.usc::rproc2fdata(n = 20, t = t, sigma = "brownian",
                           par.list = list(scale = 1, theta = 5))
fd3_d <- fda.usc::fdata.deriv(fd3)

# Functional data in one matrix and first order derivatives in another matrix
funcdata <- rbind(fd1$data, fd2$data, fd3$data)
funcderivs <- rbind(fd1_d$data, fd2_d$data, fd3_d$data)

fkwc_multisample(data = funcdata,
                 derivs = funcderivs,
                 g = factor(rep(1:3, each = 20)),
                 p = 1000)
#> $statistic
#> [1] 38.56262
#> 
#> $pvalue
#> [1] 4.228953e-09
#> 
#> $method
#> [1] "FKWC multi-sample hypothesis test"
#>