IWT1: One population Interval Wise Testing procedure
In alessiapini/fdatest: Interval Wise Testing for Functional Data

ITP1bspline

R Documentation

One population Interval Wise Testing procedure

Description

The function implements the Interval Wise Testing procedure for testing the center of symmetry of a functional population. 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

ITP1bspline(data, mu = 0, B = 1000, order = 2, nknots = dim(data)[2])

ITP1fourier(data, mu = 0, B = 1000, maxfrequency = floor(dim(data)[2]/2))

IWT1(data, mu = 0, B = 1000, dx = NULL, recycle = TRUE)

Arguments

`data`	Either pointwise evaluations of the functional data set on a uniform grid, or an `fd`. If pointwise evaluations are provided, `data` is a matrix of dimensions `c(n, J)`, with `J` evaluations on columns and `n` units on rows.
`mu`	The center of symmetry 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 containing one function. Defaults to `0`.
`B`	The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. Defaults to `1000L`.
`order`	Order of the B-spline basis expansion. Defaults to `2L`.
`nknots`	Number of knots of the B-spline basis expansion. Defaults to `dim(data)[2]`.
`maxfrequency`	The maximum frequency to be used in the Fourier basis expansion of data. Defaults to `floor(dim(data)[2] / 2)`, leading to an interpolating expansion.
`dx`	Used only if an `fd` object is provided. In this case, `dx` is the size of the discretization step of the gridused to evaluate functional data. If set to `NULL`, a grid of size `100L` is used. Defaults to `NULL`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Defaults to `TRUE`.

Value

An object of class IWT1, which is a list containing at least the following components:

test: String vector indicating the type of test performed. In this case equal to "1pop".
mu: Evaluation on a grid of the center of symmetry under the null hypothesis (as entered by the user).
unadjusted_pval: Evaluation on a grid of the unadjusted p-value function.
pval_matrix: Matrix of dimensions c(p, p) of the p-values of the multivariate tests. The element ⁠(i,j)⁠ of matrix pval.matrix contains the p-value of the joint NPC test of the components ⁠(j,j+1,...,j+(p-i))⁠.
adjusted_pval: Evaluation on a grid of the adjusted p-value function.
data.eval: Evaluation on a grid of the functional data.

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.

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

Examples

# Performing the IWT for one population
IWT.result <- IWT1(NASAtemp$paris, mu = 4, B = 10L)

# Plotting the results of the IWT
plot(IWT.result, xrange = c(0, 12), main = 'Paris temperatures')

# Plotting the p-value heatmap
IWTimage(IWT.result, abscissa_range = c(0, 12))

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

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