simu_data dataset

Simulated two Gaussian Dataset

A functional dataset where the individual functions are given by: c("$y_i(t)\n$", "$= z_{i,1} e^{-(t-1.5)^2/2} + z_{i,2}e^{-(t+1.5)^2/2}$"), c("$t \\in [-3, 3],\n$", "$~i=1,2,\\dots, 21$"), where $z_{i,1}$ and $z_{i,2}$ are i.i.d. normal with mean one and standard deviation 0.25. Each of these functions is then warped according to: c("\\gamma_i(t) = 6({e^{a_i(t+3)/6} -1 \\over e^{a_i} -\n", "1}) - 3") if $a_i \neq 0$, otherwise $\gamma_i = \gamma_{id}$

($gamma_{id}(t) = t$) is the identity warping). The variables are as follows: f containing the 21 functions of 101 samples and time which describes the sampling. data

Format

simu_data

A list with 2 components:

• f: A numeric matrix of shape $101 \times 21$ storing a sample of size $N = 21$ of curves evaluated on a grid of size $M = 101$.
• time: A numeric vector of size $M = 101$ storing the grid on which the curves f have been evaluated.

simu_data