This function computes the Epigraphic Index (EI) of elements of a univariate functional dataset.
EI(Data)
# S3 method for fData
EI(Data)
# S3 method for default
EI(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 EI 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 EI, i.e.:
$$EI( X(t) ) = \frac{1}{N} \sum_{i=1}^N I( G( X_i(t) ) \subset epi( X(t) ) ) = \frac{1}{N} \sum_{i=1}^N I( X_i(t) \geq X(t), \ \ \forall t \in I), $$
where \(G(X_i(t))\) indicates the graph of \(X_i(t)\), \(epi( X(t))\) indicates the epigraph of \(X(t)\).
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 )
EI( fD )
#> [1] 0.15 0.50 0.05 0.45 0.30 0.25 0.45 0.50 0.10 0.10 0.15 0.15 0.50 0.10 0.05
#> [16] 0.50 0.50 0.50 0.90 0.10
EI( Data )
#> [1] 0.15 0.50 0.05 0.45 0.30 0.25 0.45 0.50 0.10 0.10 0.15 0.15 0.50 0.10 0.05
#> [16] 0.50 0.50 0.50 0.90 0.10