# Statistical Testing for Functional Data

The `funStatTest` package implements various statistics for two sample comparison testing regarding functional data introduced and used in Smida et al 2022 .

This package is developed by:

## Installation

To install the `funStatTest` package, you can run:

``install.packages("funStatTest")``

You can also install the development version of `funStatTest` with the following command:

``remotes::install_git("https://plmlab.math.cnrs.fr/gdurif/funStatTest")``

## Documentation

See the package vignette and function manuals for more details about the package usage.

## Development

The `funStatTest` was developed using the `fusen` package . See in the `dev` sub-directory in the package sources for more information, in particular:

• the file `dev/dev_history.Rmd` describing the development process
• the file `dev/flat_package.Rmd` defining the major package functions (from which the vignette is extracted)
• the file `dev/flat_internal.Rmd` defining package internal functions

The `funStatTest` website was generated using the `pkgdown` package .

## Example

This is a basic example which shows you how to solve a common problem:

``library(funStatTest)``

### Data simulation

We simulate two samples of trajectories diverging by a delta function.

``````simu_data <- simul_data(
n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 10,
delta_shape = "quadratic", distrib = "normal"
)

plot_simu(simu_data)`````` We extract the matrices of trajectories associated to each sample:

``````MatX <- simu_data\$mat_sample1
MatY <- simu_data\$mat_sample2``````

And we compute the different statistics for two sample function data comparison presented in Smida et al 2022 :

``````res <- comp_stat(MatX, MatY, stat = c("mo", "med", "wmw", "hkr", "cff"))
res
#> \$mo
#>  0.9436923
#>
#> \$med
#>  0.9469112
#>
#> \$wmw
#>  0.8940712
#>
#> \$hkr
#>            [,1]
#> T1 2.548804e+08
#> T2 7.546891e+03
#>
#> \$cff
#>  12578.81``````

We can also compute p-values associated to these statistics:

``````# small data for the example
simu_data <- simul_data(
n_point = 20, n_obs1 = 4, n_obs2 = 5, c_val = 10,
delta_shape = "constant", distrib = "normal"
)

MatX <- simu_data\$mat_sample1
MatY <- simu_data\$mat_sample2

res <- permut_pval(
MatX, MatY, n_perm = 200, stat = c("mo", "med", "wmw", "hkr", "cff"),
verbose = TRUE)
res
#> \$mo
#>  0.009950249
#>
#> \$med
#>  0.009950249
#>
#> \$wmw
#>  0.009950249
#>
#> \$hkr
#>          T1          T2
#> 0.009950249 0.009950249
#>
#> \$cff
#>  0.009950249``````

:warning: computing p-values based on permutations may take some time (for large data or when using a large number of simulations. :warning:

And we can also run a simulation-based power analysis:

``````# simulate a few small data for the example
res <- power_exp(
n_simu = 20, alpha = 0.05, n_perm = 200,
stat = c("mo", "med", "wmw", "hkr", "cff"),
n_point = 25, n_obs1 = 4, n_obs2 = 5, c_val = 10, delta_shape = "constant",
distrib = "normal", max_iter = 10000, verbose = FALSE
)
res\$power_res
#> \$mo
#>  1
#>
#> \$med
#>  1
#>
#> \$wmw
#>  1
#>
#> \$hkr
#> T1 T2
#>  1  1
#>
#> \$cff
#>  1``````
1.
Smida, Z, Cucala, L, Gannoun, A, and Durif, G 2022 A median test for functional data. Journal of Nonparametric Statistics, 34(2): 520–553. DOI: https://doi.org/10.1080/10485252.2022.2064997
2.
Rochette, S 2022 Fusen: Build a package from rmarkdown files. URL https://CRAN.R-project.org/package=fusen
3.
Wickham, H, Hesselberth, J, and Salmon, M 2022 Pkgdown: Make static HTML documentation for a package. URL https://CRAN.R-project.org/package=pkgdown