Modified Half-Region Depth for univariate functional 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

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 )

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