multiMBD: (Modified) Band Depth for multivariate functional data
In roahd: Robust Analysis of High Dimensional Data

Description Usage Arguments Details Value References See Also Examples

These functions compute the Band Depth (BD) and Modified Band Depth (MBD) of elements of a multivariate functional dataset.

multiMBD(Data, weights = "uniform", manage_ties = FALSE)

## S3 method for class 'mfData'
multiMBD(Data, weights = "uniform", manage_ties = FALSE)

## Default S3 method:
multiMBD(Data, weights = "uniform", manage_ties = FALSE)

multiBD(Data, weights = "uniform")

## S3 method for class 'mfData'
multiBD(Data, weights = "uniform")

## Default S3 method:
multiBD(Data, weights = "uniform")

`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.
`manage_ties`	a logical flag specifying whether the check for ties and the relative treatment is to be carried out while computing the MBDs in each dimension. It is directly passed to `MBD`.

Given a multivariate functional dataset composed of N elements with L components each, \mathbf{X_1} =( X^1_1(t), X^2_1(t), …, X^L_1(t)), and a set of L non-negative weights,

w_1, w_2, …, w_L, \qquad ∑_{i=1}^L w_i = 1,

these functions compute the BD and MBD of each element of the functional dataset, namely:

BD( \mathbf{X_j} ) = ∑_{i=1}^{L} w_i BD( X^i_j ), \quad \forall j = 1, … N.

MBD( \mathbf{X_j} ) = ∑_{i=1}^{L} w_i MBD( X^i_j ), \quad \forall j = 1, … N.

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

Ieva, F. and Paganoni, A. M. (2013). Depth measures for multivariate functional data, Communications in Statistics: Theory and Methods, 41, 1265-1276.

Tarabelloni, N., Ieva, F., Biasi, R. and Paganoni, A. M. (2015). Use of Depth Measure for Multivariate Functional Data in Disease Prediction: An Application to Electrocardiograph Signals, International Journal of Biostatistics, 11.2, 189-201.

MBD, BD, toListOfValues, mfData

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 ) )

multiBD( mfD, weights = 'uniform' )
multiMBD( mfD, weights = 'uniform', manage_ties = TRUE )

multiBD( mfD, weights = c( 1/3, 2/3 ))
multiMBD( mfD, weights = c( 1/3, 2/3 ), manage_ties = FALSE )

multiBD( list( Data_1, Data_2 ), weights = 'uniform')
multiMBD( list( Data_1, Data_2 ), weights = 'uniform', manage_ties = TRUE )

multiBD( list( Data_1, Data_2 ), weights = c( 1/3, 2/3 ))
multiMBD( list( Data_1, Data_2 ), weights = c( 1/3, 2/3 ), manage_ties = FALSE )