This function computes the Modified Half-Region Depth (MHRD) of elements of a univariate functional dataset.
MHRD(Data)
# S3 method for fData
MHRD(Data)
# S3 method for default
MHRD(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.
The function returns a vector containing the values of MHRD for each
element of the functional dataset provided in Data
.
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.
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.
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 )
#> [1] 0.1515 0.2830 0.4445 0.2245 0.4325 0.0985 0.5020 0.1105 0.5040 0.1420
#> [11] 0.0700 0.0985 0.3930 0.3350 0.3235 0.3435 0.4700 0.4145 0.1985 0.3675
MHRD( Data )
#> [1] 0.1515 0.2830 0.4445 0.2245 0.4325 0.0985 0.5020 0.1105 0.5040 0.1420
#> [11] 0.0700 0.0985 0.3930 0.3350 0.3235 0.3435 0.4700 0.4145 0.1985 0.3675