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Theroahd (Robust Analysis of High-dimensional Data) packageallows to use a set of statistical tools for theexploration androbustification of univariate and multivariatefunctional datasetsthrough the use of depth-based statistical methods.

In the implementation of functions, special attention was put to theirefficiency, so that they can be profitably used also for the analysis ofhigh-dimensional datasets.

For a full-featured description of the package, please take a look attheroahdvignette.

Install the released version ofroahd from CRAN:

install.packages("roahd")

Or install the development version from GitHub with:

# install.packages("remotes")remotes::install_github("astamm/roahd")

A simpleS3 representation of functional data object,fData, allowsto encapsulate the important features of univariate functional datasets(like the grid of the dependent variable, the pointwise observations,etc.):

library(roahd)# Grid representing the dependent variablegrid= seq(0,1,length.out=100 )# Pointwise measurements of the functional datasetData=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 datasetfD= fData(grid,Data )# S3 representation of a multivariate functional datasetmfD= mfData(grid,list('comp1'=Data,'comp2'=Data ) )

Also, this allows to exploit simple calls to customized functions whichsimplifies the exploratory analysis:

# Algebra of fData objectsfD+1:100fD*4fD+fD# Subsetting fData objects (providing other fData objects)fD[1, ]fD[1,2:4]# Sample mean and (depth-based) median(s)mean(fD )mean(fD[1,10:20 ] )median_fData(fD,type='MBD' )

# Plotting functionsplot(fD )plot( mean(fD ),lwd=4,add=TRUE )

plot(fD[2:3, ] )

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

• Band depths 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 correlationcoefficients for univariate and multivariate functional data.

These also are the core of the visualization / robustification toolslike functional boxplot(fbplot) andoutliergram(outliergram),allowing the visualization and identification of amplitude and shapeoutliers.

Thanks to the functions for the simulation of synthetic functionaldatasets, bothfbplot andoutliergramprocedures can be auto-tuned to the dataset at hand, in order to controlthe true positive outliers rate.

If you use this package for your own research, please cite thecorresponding R Journal article:

To cite roahd in publications use:  Ieva, F., Paganoni, A. M., Romo, J., & Tarabelloni, N. (2019). roahd  Package: Robust Analysis of High Dimensional Data. The R Journal,  11(2), pp. 291-307.A BibTeX entry for LaTeX users is  @Article{,    title = {{roahd Package: Robust Analysis of High Dimensional Data}},    author = {Francesca Ieva and Anna Maria Paganoni and Juan Romo and Nicholas Tarabelloni},    journal = {{The R Journal}},    year = {2019},    volume = {11},    number = {2},    pages = {291--307},    url = {https://doi.org/10.32614/RJ-2019-032},  }