FDR2: Two population functional Benjamini-Hochberg procedure

In alessiapini/fdatest: Interval Wise Testing for Functional Data

Two population functional Benjamini-Hochberg procedure

Description

The function implements the functional Benjamini Hochberg (fBH) 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 family-wise error rate asymptotically.

Usage

FDR2(
  data1,
  data2,
  mu = 0,
  B = 1000L,
  paired = FALSE,
  dx = NULL,
  alternative = "two.sided"
)

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.
alternative	A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".

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.

• 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

Lundtorp Olsen, N., Pini, A., & Vantini, S. (2021). False discovery rate for functional data TEST 30, 784–809.

See Also

See also plot.fdatest2 for plotting the results.

Examples

# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the fBH for two populations

FDR.result <- FDR2(NASAtemp$paris, NASAtemp$milan)

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

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

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