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 |
FD2 |
a functional data object of type |
conf.level |
confidence level of the test. |
stat_test |
the chosen test statistic to be used: |
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | # 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 - Loève 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 )
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