gmfd_diss {gmfd}

Dissimilarity matrix function

Description

This function computes the dissimilarity matrix containing the distances between the curves of the functional dataset

Usage

gmfd_diss(FD, metric, p = NULL, k_trunc = NULL)

Arguments

FD

a functional data object of type funData

metric

the chosen distance to be used. Choose "L2" for the classical L2-distance, "trunc" for the truncated Mahalanobis semi-distance, "mahalanobis" for the generalized Mahalanobis distance.

p

a positive numeric value containing the parameter of the regularizing function for the generalized Mahalanobis distance.

k_trunc

a positive numeric value representing the number of components at which the truncated mahalanobis distance must be truncated

Value

The function returns a matrix of numeric values containing the distances between the curves.

References

Ghiglietti A., Ieva F., Paganoni A. M. (2017). Statistical inference for stochastic processes: Two-sample hypothesis tests, Journal of Statistical Planning and Inference, 180:49-68.

Ghiglietti A., Paganoni A. M. (2017). Exact tests for the means of gaussian stochastic processes. Statistics & Probability Letters, 131:102–107.

Examples

# Define parameters
n <- 50
P <- 100
K <- 150

# Grid of the functional dataset
t <- seq( 0, 1, length.out = P )

# Define the means and the parameters to use in the simulation
m1 <- t^2 * ( 1 - t )

rho <- rep( 0, K )
theta <- matrix( 0, K, P )
for ( k in 1:K ) {
  rho[k] <- 1 / ( k + 1 )^2
  if ( k%%2 == 0 )
    theta[k, ] <- sqrt( 2 ) * sin( k * pi * t )
  else if ( k%%2 != 0 && k != 1 )
    theta[k, ] <- sqrt( 2 ) * cos( ( k - 1 ) * pi * t )
  else
    theta[k, ] <- rep( 1, P )
}

# Simulate the functional data
x <- gmfd_simulate( n, m1, rho = rho, theta = theta )

FD <- funData( t, x )

D <- gmfd_diss( FD, metric = "L2" )