ITP1bspline | R Documentation |
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.
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)
data |
Either pointwise evaluations of the functional data set on a
uniform grid, or an |
mu |
The center of symmetry under the null hypothesis. Three
possibilities are available for
|
B |
The number of iterations of the MC algorithm to evaluate the
p-values of the permutation tests. Defaults to |
order |
Order of the B-spline basis expansion. Defaults to |
nknots |
Number of knots of the B-spline basis expansion. Defaults to
|
maxfrequency |
The maximum frequency to be used in the Fourier basis
expansion of data. Defaults to |
dx |
Used only if an |
recycle |
Flag used to decide whether the recycled version of the IWT
should be used (see Pini and Vantini, 2017 for details). Defaults to
|
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.
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.
See also plot.IWT1
and IWTimage
for
plotting the results.
# 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)
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