ITP1fourier: One population Interval Testing Procedure with Fourier basis

Description Usage Arguments Value References See Also Examples

Description

The function implements the Interval Testing Procedure for testing the center of symmetry of a functional population evaluated on a uniform grid. Data are represented by means of the Fourier expansion and the significance of each basis coefficient is tested with an interval-wise control of the Family Wise Error Rate.

Usage

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ITP1fourier(data, mu = 0, maxfrequency = floor(dim(data)[2]/2), B = 10000)

Arguments

data

Pointwise evaluations of the functional data set on a uniform grid. It 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: either a constant (in this case, a constant function is used) or a J-dimensional vector containing the evaluations on the same grid which data are evaluated. The default is mu=0.

maxfrequency

The maximum frequency to be used in the Fourier basis expansion of data. The default is floor(dim(data)[2]/2), leading to an interpolating expansion.

B

The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is B=1000.

Value

ITP1fourier returns an object of class "ITP1". An object of class "ITP1" is a list containing at least the following components:

basis

String vector indicating the basis used for the first phase of the algorithm. In this case equal to "Fourier".

test

String vector indicating the type of test performed. In this case equal to "1pop".

mu

Center of symmetry under the null hypothesis (as entered by the user).

coeff

Matrix of dimensions c(n,p) of the p coefficients of the B-spline basis expansion. Rows are associated to units and columns to the basis index.

pval

Unadjusted p-values for each basis coefficient.

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

Adjusted p-values for each basis coefficient.

labels

Labels indicating the population membership of each data (in this case always equal to 1).

data.eval

Evaluation on a fine uniform grid of the functional data obtained through the basis expansion.

heatmap.matrix

Heatmap matrix of p-values (used only for plots).

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.

See Also

See also plot.ITP1 and ITPimage for plotting the results, ITP1bspline for ITP based on B-spline basis, IWT1 for a one-sample test that is not based on an a-priori selected basis expansion.

Examples

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# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the ITP
ITP.result <- ITP1fourier(NASAtemp$milan,maxfrequency=20,B=1000)

# Plotting the results of the ITP
plot(ITP.result,main='NASA data',xrange=c(1,365),xlab='Day')

# Plotting the p-value heatmap
ITPimage(ITP.result,abscissa.range=c(1,365))

# Selecting the significant coefficients
which(ITP.result$adjusted.pval < 0.05)

alessiapini/fdatest documentation built on May 9, 2019, 1:06 a.m.