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`

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.):

```
# 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:

- Band Dephts 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 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.