roahd (version 1.4.3)

MHRD: Modified Half-Region Depth for univariate functional data

Description

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

Usage

MHRD(Data)
# S3 method for fData
MHRD(Data)
# S3 method for default
MHRD(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.

Value

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

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 MHRD of its elements, i.e.:

$$MHRD(X(t)) = \min( MEI( X(t) ), MHI(X(t)) ),$$

where \(MEI(X(t))\) indicates the Modified Epigraph Index (MEI) of \(X(t)\) with respect to the dataset, and \(MHI(X(t))\) indicates the Modified Hypograph Index of \(X(t)\) with respect to the dataset.

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

HRD, MEI, MHI

Examples

# NOT RUN {
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 )

MHRD( fD )

MHRD( Data )

# }