Global2: Two population Global Testing procedure

In alessiapini/fdatest: Interval Wise Testing for Functional Data

Two population Global Testing procedure

Description

The function implements the Global Testing procedure for testing mean differences between two functional populations. Functional data are tested locally and unadjusted and adjusted p-value functions are provided. The unadjusted p-value function controls the point-wise error rate. The adjusted p-value function controls the interval-wise error rate.

Usage

Global2(
  data1,
  data2,
  mu = 0,
  B = 1000L,
  paired = FALSE,
  dx = NULL,
  stat = "Integral"
)

Arguments

data1	First population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a fd object from the package fda. If pointwise evaluations are provided, data2 is a matrix of dimensions c(n1,J), with J evaluations on columns and n1 units on rows.
data2	Second population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a fd object from the package fda. If pointwise evaluations are provided, data2 is a matrix of dimensions c(n1,J), with J evaluations on columns and n2 units on rows.
mu	Functional mean difference under the null hypothesis. Three possibilities are available for mu: a constant (in this case, a constant function is used); a J-dimensional vector containing the evaluations on the same grid which data are evaluated; a fd object from the package fda containing one function. The default is mu=0.
B	The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is B=1000.
paired	A logical indicating whether a paired test has to be performed. Default is FALSE.
dx	Used only if a fd object is provided. In this case, dx is the size of the discretization step of the grid used to evaluate functional data. If set to NULL, a grid of size 100 is used. Default is NULL.
stat	Test statistic used for the global test. Possible values are: "Integral": integral of the squared sample mean difference; "Max": maximum of the squared sample mean difference; "Integral_std": integral of the squared t-test statistic; "Max_std": maximum of the squared t-test statistic. Default is "Integral".

Value

An object of class fdatest2, containing the following components:

• test: String vector indicating the type of test performed. In this case equal to "2pop".

• mu: Evaluation on a grid of the functional mean difference under the null hypothesis (as entered by the user).

• unadjusted_pval: Evaluation on a grid of the unadjusted p-value function (it is a constant function according to the global testing procedure).

• adjusted_pval: Evaluation on a grid of the adjusted p-value function.

• data.eval: Evaluation on a grid of the functional data.

• ord_labels: Vector of labels indicating the group membership of data.eval.

References

A. Pini and S. Vantini (2017). The Interval Testing Procedure: Inference for Functional Data Controlling the Family Wise Error Rate on Intervals. Biometrics 73(3): 835–845.

Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424

See Also

See also IWT2 for local inference. See plot.fdatest2 for plotting the results.

Examples

# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the Global for two populations
Global.result <- Global2(NASAtemp$paris, NASAtemp$milan)

# Plotting the results of the Global
plot(
  Global.result, 
  xrange = c(0, 12), 
  main = 'Global results for testing mean differences'
)

# Selecting the significant components at 5% level
which(Global.result$adjusted_pval < 0.05)

alessiapini/fdatest documentation built on Jan. 4, 2025, 5:37 a.m.