stat_hkr {funStatTest}

Horváth-Kokoszka-Reeder statistics

Description

The Horváth-Kokoszka-Reeder statistics defined in Chakraborty & Chaudhuri (2015) (and noted HKR1 and HKR2 in Smida et al 2022) are computed to compare two sets of functional trajectories.

Usage

stat_hkr(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

A list with the following elements

• T1: numeric value corresponding to the HKR1 statistic value

• T2: numeric value corresponding to the HKR2 statistic value

• eigenval: numeric vector of eigen values from the empirical pooled covariance matrix of MatX and MatY (see Smida et al, 2022, for more details)

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

Horváth, L., Kokoszka, P., & Reeder, R. (2013). Estimation of the mean of functional time series and a two-sample problem. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 75(1), 103–122. doi:10.1111/j.1467-9868.2012.01032.x

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()

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_hkr(MatX, MatY)