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Wilcoxon-Mann-Whitney (WMW) statistic

stat_wmw.Rd

The Wilcoxon-Mann-Whitney statistic defined in Chakraborty & Chaudhuri (2015) (and noted WMW in Smida et al 2022) is computed to compare two sets of functional trajectories.

Usage

stat_wmw(MatX, MatY)

Arguments

MatX

numeric matrix of dimension n_point x n containing n trajectories (in columns) of size n_point (in rows).

MatY

numeric matrix of dimension n_point x m containing m trajectories (in columns) of size n_point (in rows).

Value

numeric value corresponding to the WMW statistic value

References

Anirvan Chakraborty, Probal Chaudhuri, A Wilcoxon–Mann–Whitney-type test for infinite-dimensional data, Biometrika, Volume 102, Issue 1, March 2015, Pages 239–246, doi:10.1093/biomet/asu072

Zaineb Smida, Lionel Cucala, Ali Gannoun & Ghislain Durif (2022) A median test for functional data, Journal of Nonparametric Statistics, 34:2, 520-553, doi:10.1080/10485252.2022.2064997 , hal-03658578

See also

comp_stat(), permut_pval()

Author

Zaineb Smida, Ghislain DURIF, Lionel Cucala

Examples

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

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

stat_wmw(MatX, MatY)
#> [1] 0.998492