The **roahd** (*Robust Analysis of High-dimensional Data*) package 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 take a look at the roahd vignette.

Install the released version of **roahd** from CRAN:

`install.packages("roahd")`

Or install the development version from GitHub with:

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

`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.):

```
library(roahd)
# 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 customized functions which simplifies the exploratory analysis:

```
# Algebra of fData objects
fD + 1 : 100
fD * 4
fD + 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' )
```

`plot( fD[ 2:3, ] )`

A part of the package is specifically devoted to the computation of depths 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 correlation coefficients for univariate and multivariate 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 and 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.

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

```
in publications use:
To cite roahd
& Tarabelloni, N. (2019). roahd
Ieva, F., Paganoni, A. M., Romo, J., : Robust Analysis of High Dimensional Data. The R Journal,
Package11(2), pp. 291-307.
for LaTeX users is
A BibTeX entry
@Article{,
= {{roahd Package: Robust Analysis of High Dimensional Data}},
title = {Francesca Ieva and Anna Maria Paganoni and Juan Romo and Nicholas Tarabelloni},
author = {{The R Journal}},
journal = {2019},
year = {11},
volume = {2},
number = {291--307},
pages = {https://doi.org/10.32614/RJ-2019-032},
url }
```