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`

objectsA 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' )
```

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

```
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 Kendallâ€™s correlation indexes for functional data,
- Confidence intervals and tests on Spearmanâ€™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:

```
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},
}
```

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