gmfd_test {gmfd}

Two-sample hypotesis tests

Description

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

Usage

gmfd_test(FD1, FD2, conf.level = 0.95, stat_test, p = NULL,
  k_trunc = NULL)

Arguments

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.

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 list with the following components:

statistic the value of the test statistic.

quantile the value of the quantile.

p.value the p-value for the test.

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

See Also

funDist

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 )
}

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

m2 <- m1 + 0.1 * s

# Simulate the functional data
x1 <- gmfd_simulate( n, m1, rho = rho, theta = theta )
x2 <- gmfd_simulate( n, m2, rho = rho, theta = theta )
FD1 <- funData( t, x1 )
FD2 <- funData( t, x2 )
output <- gmfd_test( FD1, FD2, 0.95, "mahalanobis", p = 10^5 )