HRD: Half-Region Depth for univariate functional data
In roahd: Robust Analysis of High Dimensional Data

Description Usage Arguments Details Value References See Also Examples

This function computes the Half-Region Depth (HRD) of elements of a univariate functional dataset.

HRD(Data)

## S3 method for class 'fData'
HRD(Data)

## Default S3 method:
HRD(Data)

Data

either an fData object or a matrix-like dataset of functional data (e.g. fData$values), with observations as rows and measurements over grid points as columns.

Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t), defined over a compact interval I=[a,b], this function computes the HRD of its elements, i.e.:

HRD(X(t)) = \min( EI( X(t) ), HI(X(t)) ),

where EI(X(t)) indicates the Epigraph Index (EI) of X(t) with respect to the dataset, and HI(X(t)) indicates the Hypograph Index of X(t) with respect to the dataset.

The function returns a vector containing the values of HRD for each element of the functional dataset provided in Data.

Lopez-Pintado, S. and Romo, J. (2012). A half-region depth for functional data, Computational Statistics and Data Analysis, 55, 1679-1695.

Arribas-Gil, A., and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram, Biostatistics, 15(4), 603-619.

MHRD, EI, HI, fData

N = 20
P = 1e2

grid = seq( 0, 1, length.out = P )

C = exp_cov_function( grid, alpha = 0.2, beta = 0.3 )

Data = generate_gauss_fdata( N,
                             centerline = sin( 2 * pi * grid ),
                             C )

fD = fData( grid, Data )

HRD( fD )

HRD( Data )