gmfd_test2: Two-sample hypotesis tests
In martinoandrea92/dpdistance: Inference and Clustering of Functional Data

Description Usage Arguments Value References See Also Examples

Performs a two sample hypotesis tests on two samples of functional data.

1	gmfd_test2(FD1, FD2, conf.level = 0.95, stat_test, p = NULL)

`FD1`	a functional data object of type `funData` of the first sample.
`FD2`	a functional data object of type `funData` of the second sample.
`conf.level`	confidence level of the test.
`stat_test`	the chosen test statistic to be used: `"L2"` for the classical L2-distance, `"L2_trunc"` for the truncated L2-distance, `"trunc"` for the truncated Mahalanobis semi-distance, `"mahalanobis"` for the generalized Mahalanobis distance
`p`	a vector of positive numeric value containing the parameters of the regularizing function for the generalized Mahalanobis distance.

The function returns a list with the following components:

statistic the value of the test statistic.

p.value the p-value for the test.

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. Statics & Probability Letters, 131:102–107.

funDist

# 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
# with the Karhunen - LoÃ¨ve expansion
m1 <- t^2 * ( 1 - t )

lambda <- rep( 0, K )
theta <- matrix( 0, K, P )
for ( k in 1:K) {
  lambda[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 )
}

s <- 0
for (k in 4:K) {
 s <- s + sqrt( lambda[k] )*theta[k,]
}

m2 <- m1 + 0.1*s

# Simulate the functional data
x1 <- simulate_KL( t, n, m1, rho = lambda, theta = theta )
x2 <- simulate_KL( t, n, m2, rho = lambda, theta = theta )

output <- gmfd_test2( x1, x2, 0.95, "L2", 1 )