HI {roahd} | R Documentation |
Hypograph Index of univariate functional dataset
Description
This function computes the Hypograph Index (HI) of elements of a univariate functional dataset.
Usage
HI(Data)
## S3 method for class 'fData'
HI(Data)
## Default S3 method:
HI(Data)
Arguments
Data |
either an |
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
HI, i.e.:
HI( X(t) ) = \frac{1}{N} \sum_{i=1}^N I( G( X_i(t) ) \subset
hyp( X(t) ) ) = \frac{1}{N} \sum_{i=1}^N I( X_i(t) \leq X(t), \ \
\forall t \in I),
where G(X_i(t))
indicates the graph of X_i(t)
, hyp( X(t))
indicates the hypograph of X_i(t)
.
Value
The function returns a vector containing the values of HI 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
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 )
HI( fD )
HI( Data )