HRD {roahd}

Half-Region Depth for univariate functional data

Description

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

Usage

HRD(Data)

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

## Default S3 method:
HRD(Data)

Arguments

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.

Details

Given a univariate functional dataset, X_1(t), X_2(t), \ldots, 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.

Value

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

References

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.

See Also

MHRD, EI, HI, fData

Examples

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 )