# multiMHI: Modified Hypograph Index for multivariate functional data In roahd: Robust Analysis of High Dimensional Data

## Description

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

## Usage

 1 2 3 4 5 6 7 multiMHI(Data, weights = "uniform") ## S3 method for class 'mfData' multiMHI(Data, weights = "uniform") ## Default S3 method: multiMHI(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.

## Details

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 MHI of each element of the functional dataset, namely:

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

## Value

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

mfData, MHI, MEI, multiMEI
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 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 multiMHI( mfD, weights = 'uniform' ) # Non-uniform, custom weights multiMHI( mfD, weights = c(2/3, 1/3) )