roahd

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)

fData and mfData objects

A simple S3 representation of functional data object, fData, 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, :] )

Robust methods for functional data analysis

A part of the package is specifically devoted to the computation of depths and other statistical indexes for functional data:

• Band Dephts and Modified Band Depths,
• Modified band depths for multivariate functional data,
• Epigraph and Hypograph indexes,
• Spearman and Kendall’s correlation indexes for functional data.
• Confidence intervals and tests on Spearman’s correlation coefficients for univariate andmultivariate functional data.

These also are the core of the visualization/robustification tools like functional boxplot (fbplot) and outliergram (outliergram), allowing the visualization and identification of amplitude/shape outliers.

Thanks to the functions for the simulation of synthetic functional datasets, both fbplot and outliergram procedures can be auto-tuned to the dataset at hand, in order to control the true positive outliers rate.