roahd (version 1.4.3)

multiMEI: Modified Epigraph Index for multivariate functional data

Description

These functions compute the Modified Epigraph Index of elements of a multivariate functional dataset.

Usage

multiMEI(Data, weights = "uniform")
# S3 method for mfData
multiMEI(Data, weights = "uniform")
# S3 method for default
multiMEI(Data, weights = "uniform")

Arguments

Data

specifies the the multivariate functional dataset. It is either an object of class mfData or a list of 2-dimensional matrices having as rows the elements of that component and as columns the measurements of the functional data over the grid.

weights

either a set of weights (of the same length of Data ) or the string "uniform" specifying that a set of uniform weights (of value $1/L$, where $L$ is the number of dimensions of the functional dataset and thus the length of Data) is to be used.

Value

The function returns a vector containing the values of MEI of each element of the multivariate functional dataset.

Details

Given a multivariate functional dataset composed of $N$ elements with $L$ components each, ${\mathbf{X}}_{\mathbf{1}}=(X_1^1(t),$ $X_1^2(t),\dots ,X_1^L(t))$, and a set of $L$ non-negative weights,

$$w_1,w_2,\dots ,w_L,\sum _{i=1}^L{w}_i=1,$$

these functions compute the MEI of each element of the functional dataset, namely:

$$MEI({\mathbf{X}}_{\mathbf{j}})=\sum _{i=1}^L{w}_{i}MEI(X_j^i),\mathrm{\forall }j=1,\dots N.$$

See Also

mfData, MEI, MHI, multiMHI

Examples

# NOT RUN {
N = 20
P = 1e3

grid = seq( 0, 10, length.out = P )

# Generating an exponential covariance function to be used to simulate gaussian
# functional data
Cov = exp_cov_function( grid, alpha = 0.2, beta = 0.8 )

# First component of the multivariate guassian functional dataset
Data_1 = generate_gauss_fdata( N, centerline = rep( 0, P ), Cov = Cov )

# First component of the multivariate guassian functional dataset
Data_2 = generate_gauss_fdata( N, centerline = rep( 0, P ), Cov = Cov )

mfD = mfData( grid, list( Data_1, Data_2 ) )

# Uniform weights
multiMEI( mfD, weights = 'uniform' )

# Non-uniform, custom weights
multiMEI( mfD, weights = c(2/3, 1/3) )

# }