Package roahd (Robust Analysis of High-dimensional Data) allows to use a set of statistical tools for the exploration and robustification of univariate and multivariate functional datasets through the use of depth-based statistical methods.
In the implementation of functions special attention was put to their efficiency, so that they can be profitably used also for the analysis of high-dimensional datasets.
(For a full-featured description of the package, please turn to the Vignette)
S3 representation of functional data object,
allows to encapsulate the important features of univariate functional datasets (like the
grid of the dependent variable, the pointwise observations etc.):
# Grid representing the dependent variable grid = seq( 0, 1, length.out = 100 ) # Pointwise-measurements of the functional dataset Data = matrix( c( sin( 2 * pi * grid ), cos ( 2 * pi * grid ), sin( 2 * pi * grid + pi / 4 ) ), ncol = 100, byrow = TRUE ) # S3 object encapsulating the univariate functional dataset fD = fData( grid, Data ) # S3 representation of a multivariate functional dataset mfD = mfData( grid, list( 'comp1' = Data, 'comp2' = Data ) )
Also, this allows to exploit simple calls to customised functions which simplify the exploratory analysis:
# Algebra of fData objects fD + 1 : 100 fD * 4 fD_1 + fD_2 # Subsetting fData objects (providing other fData objects) fD[ 1, ] fD[ 1, 2 : 4] # Smaple mean and (depth-based) median(s) mean( fD ) mean( fD[ 1, 10 : 20 ] ) median_fData( fD, type = 'MBD' ) # Plotting functions plot( fD ) plot( mean( fD ), add = TRUE ) plot( fD[ 2:3, :] )
A part of the package is specifically devoted to the computation of depths and other statistical indexes for functional data:
These also are the core of the visualization/robustification tools like
functional boxplot (
fbplot) and outliergram (
the visualization and identification of amplitude/shape outliers.
Thanks to the functions for the simulation of synthetic functional datasets,
outliergram procedures can be auto-tuned to the dataset
at hand, in order to control the true positive outliers rate.
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