IWT1: One population Interval Wise Testing procedure

Description Usage Arguments Value References See Also Examples

View source: R/IWT1.R

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

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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 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.

Value

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.

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 plot.IWT1 and IWTimage for plotting the results.

Examples

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# 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)

alessiapini/fdatest documentation built on Oct. 30, 2020, 8:15 a.m.