Package 'funStatTest'

Title: Statistical Testing for Functional Data
Description: Implementation of two sample comparison procedures based on median-based statistical tests for functional data, introduced in Smida et al (2022) <doi:10.1080/10485252.2022.2064997>. Other competitive state-of-the-art approaches proposed by Chakraborty and Chaudhuri (2015) <doi:10.1093/biomet/asu072>, Horvath et al (2013) <doi:10.1111/j.1467-9868.2012.01032.x> or Cuevas et al (2004) <doi:10.1016/j.csda.2003.10.021> are also included in the package, as well as procedures to run test result comparisons and power analysis using simulations.
Authors: Zaineb Smida [aut] , Ghislain Durif [aut, cre] , Lionel Cucala [aut]
Maintainer: Ghislain Durif <[email protected]>
License: AGPL (>= 3)
Version: 1.0.3
Built: 2025-02-18 04:11:32 UTC
Source: https://github.com/cran/funStatTest

Help Index

Compute multiple statistics

Description

Computation of the different statistics defined in the package. See Smida et al (2022) for more details.

Usage

comp_stat(MatX, MatY, stat = c("mo", "med"))

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).
stat

character string or vector of character string, name of the statistics for which the p-values will be computed, among "mo", "med", "wmw", "hkr", "cff".

Details

For HKR statistics, only the values of the two statistics, namely HKR1 and HKR2 and not the eigen values (see stat_hkr() for more details).

Value

list of named numeric value corresponding to the statistic values listed in stat input.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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

stat_mo(), stat_med(), stat_wmw(), stat_hkr(), stat_cff()

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

res <- comp_stat(MatX, MatY, stat = c("mo", "med", "wmw", "hkr", "cff"))
res

Permutation-based computation of p-values

Description

Computation of the p-values associated to any statistics described in the package with the permutation methods. See Smida et al (2022) for more details.

Usage

permut_pval(MatX, MatY, n_perm = 100, stat = c("mo", "med"), verbose = FALSE)

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).
n_perm

integer, number of permutation to compute the p-values.
stat

character string or vector of character string, name of the statistics for which the p-values will be computed, among "mo", "med", "wmw", "hkr", "cff".
verbose

boolean, if TRUE, enable verbosity.

Value

list of named numeric value corresponding to the p-values for each statistic listed in the stat input.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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

stat_mo(), stat_med(), stat_wmw(), stat_hkr(), stat_cff(), comp_stat()

Examples

# simulate 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 = 100, stat = c("mo", "med", "wmw", "hkr", "cff"), 
    verbose = TRUE)
res

Graphical representation of simulated data

Description

Graphical representation of simulated data

Usage

plot_simu(simu)

Arguments

simu

list, output of simul_data()

Value

the ggplot2 graph of simulated tajectories.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

See Also

simul_data()

Examples

# constant delta
simu_data <- simul_data(
    n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 5, 
    delta_shape = "constant", distrib = "normal"
)
plot_simu(simu_data)
# linear delta
simu_data <- simul_data(
    n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 5, 
    delta_shape = "linear", distrib = "normal"
)
plot_simu(simu_data)
# quadratic delta
simu_data <- simul_data(
    n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 5, 
    delta_shape = "quadratic", distrib = "normal"
)
plot_simu(simu_data)

Simulation-based experiment for power analysis

Description

Computation of the statistical power (i.e. risk to reject the null hypothesis when it is false) associated to any statistics described in the package based on simulation permutation-based p-values computations. See Smida et al (2022) for more details.

Usage

power_exp(
  n_simu = 100,
  alpha = 0.05,
  n_perm = 100,
  stat = c("mo", "med"),
  n_point = 100,
  n_obs1 = 50,
  n_obs2 = 50,
  c_val = 1,
  delta_shape = "constant",
  distrib = "normal",
  max_iter = 10000,
  verbose = FALSE
)

Arguments

n_simu

integer value, number of simulations to compute the statistical power.
alpha

numerical value, between 0 and 1, type I risk level to reject the null hypothesis in the simulation. Default value is ⁠5%⁠.
n_perm

integer, number of permutation to compute the p-values.
stat

character string or vector of character string, name of the statistics for which the p-values will be computed, among "mo", "med", "wmw", "hkr", "cff".
n_point

integer value, number of points in the trajectory.
n_obs1

integer value, number of trajectories in the first sample.
n_obs2

integer value, number of trajectories in the second sample.
c_val

numeric value, level of divergence between the two samples.
delta_shape

character string, shape of the divergence between the two samples, among "constant", "linear", "quadratic".
distrib

character string, type of probability distribution used to simulate the data among "normal", "cauchy", "dexp", "student".
max_iter

integer, maximum number of iteration for the iterative simulation process.
verbose

boolean, if TRUE, enable verbosity.

Details

The c_val input argument should be strictly positive so that the null hypothesis is not verified when simulating the data (i.e. so that the two sample are not generated from the same probability distribution).

Value

a list with the following elements:

  • power_res: a list of named numeric value corresponding to the power values for each statistic listed in stat input.

  • pval_res: a list of named numeric values corresponding to the p-values for each simulation and each statistic listed in the stat input.

  • simu_config: information about input parameters used for simulation, including n_simu, c_val, distrib, delta_shape, n_point, n_obs1, n_obs2.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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

stat_mo(), stat_med(), stat_wmw(), stat_hkr(), stat_cff(), comp_stat()

Examples

# simulate a few small data for the example
res <- power_exp(
    n_simu = 20, alpha = 0.05, n_perm = 100, 
    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

Simulation of trajectories from two samples diverging by a delta function

Description

Simulate n_obs1 trajectories of length n_point in the first sample and n_obs2 trajectories of length n_point in the second sample.

Usage

simul_data(
  n_point,
  n_obs1,
  n_obs2,
  c_val = 0,
  delta_shape = "constant",
  distrib = "normal",
  max_iter = 10000
)

Arguments

n_point

integer value, number of points in the trajectory.
n_obs1

integer value, number of trajectories in the first sample.
n_obs2

integer value, number of trajectories in the second sample.
c_val

numeric value, level of divergence between the two samples.
delta_shape

character string, shape of the divergence between the two samples, among "constant", "linear", "quadratic".
distrib

character string, type of probability distribution used to simulate the data among "normal", "cauchy", "dexp", "student".
max_iter

integer, maximum number of iteration for the iterative simulation process.

Value

A list with the following elements

  • mat_sample1: numeric matrix of dimension ⁠n_point x n_obs1⁠ containing n_obs1 trajectories (in columns) of size n_point (in rows) corresponding to sample 1.

  • mat_sample2: numeric matrix of dimension ⁠n_point x n_obs2⁠ containing n_obs2 trajectories (in columns) of size n_point (in rows) corresponding to sample 2.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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

plot_simu(), simul_traj()

Examples

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

Single trajectory simulation

Description

Simulate a trajectory of length n_point using a random generator associated to different probability distribution.

Usage

simul_traj(n_point, distrib = "normal", max_iter = 10000)

Arguments

n_point

integer value, number of points in the trajectory.
distrib

character string, type of probability distribution used to simulate the data among "normal", "cauchy", "dexp", "student".
max_iter

integer, maximum number of iteration for the iterative simulation process.

Value

Vector of size n_point with the trajectory values.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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

simul_data()

Examples

simu_vec <- simul_traj(100)
plot(simu_vec, xlab = "point", ylab = "value")

Cuevas-Febrero-Fraiman statistic

Description

The Cuevas-Febrero-Fraiman statistics defined in Cuevas et al (2004) (and noted CFF in Smida et al 2022) is computed to compare two sets of functional trajectories.

Usage

stat_cff(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

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

Cuevas, A, Febrero, M, and Fraiman, R (2004) An anova test for functional data. Computational Statistics & Data Analysis, 47(1): 111–122. doi:10.1016/j.csda.2003.10.021

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_cff(MatX, MatY)

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)

MED median statistic

Description

The MED median statistics defined in Smida et al (2022) is computed to compare two sets of functional trajectories.

Usage

stat_med(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 MED median statistic value

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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_med(MatX, MatY)

MO median statistic

Description

The MO median statistics defined in Smida et al (2022) is computed to compare two sets of functional trajectories.

Usage

stat_mo(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 MO median statistic value

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

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_mo(MatX, MatY)

Wilcoxon-Mann-Whitney (WMW) statistic

Description

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

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

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()

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)