ITP2fourier | R Documentation |
The function implements the Interval Testing Procedure for testing the difference between two functional populations evaluated on a uniform grid. Data are represented by means of the Fourier basis and the significance of each basis coefficient is tested with an interval-wise control of the Family Wise Error Rate.
ITP2fourier( data1, data2, mu = 0, maxfrequency = floor(dim(data1)[2]/2), B = 10000, paired = FALSE )
data1 |
Pointwise evaluations of the first population's functional data set on a uniform grid. |
data2 |
Pointwise evaluations of the second population's functional data set on a uniform grid. |
mu |
The difference between the first functional population and the second functional population under the null hypothesis. Either a constant (in this case, a constant function is used) or a |
maxfrequency |
The maximum frequency to be used in the Fourier basis expansion of data. The default is |
B |
The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is |
paired |
A logical indicating whether the test is paired. The default is |
ITP2fourier
returns an object of class
"ITP2
".
An object of class "ITP2
" 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 |
test |
String vector indicating the type of test performed. In this case equal to |
mu |
Difference between the first functional population and the second functional population under the null hypothesis (as entered by the user). |
paired |
Logical indicating whether the test is paired (as entered by the user). |
coeff |
Matrix of dimensions |
pval |
Unadjusted p-values for each basis coefficient. |
pval.matrix |
Matrix of dimensions |
adjusted.pval |
Adjusted p-values for each basis coefficient. |
labels |
Labels indicating the population membership of each data. |
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). |
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 plot.ITP2
and ITPimage
for plotting the results,
ITP2bspline
for ITP based on B-spline basis, IWT2
for a two-sample test that is not based on
an a-priori selected basis expansion.
# Importing the NASA temperatures data set data(NASAtemp) # Performing the ITP ITP.result <- ITP2fourier(NASAtemp$milan,NASAtemp$paris,maxfrequency=20,B=1000,paired=TRUE) # 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)
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