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

Description Usage Arguments Value References See Also Examples

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.

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

`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, `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 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`.
`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`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Default is `TRUE`.

IWT1 returns an object of class "IWT1". An object of class "IWT1" 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.

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 plot.IWT1 and IWTimage for plotting the results.

# Importing the NASA temperatures data set
data(NASAtemp)

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

# 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)