generate_gauss_fdata: Generation of gaussian univariate functional data
In roahd: Robust Analysis of High Dimensional Data

Description Usage Arguments Details Value See Also Examples

generate_gauss_fdata generates a dataset of univariate functional data with a desired mean and covariance function.

1	generate_gauss_fdata(N, centerline, Cov = NULL, CholCov = NULL)

`N`	the number of distinct functional observations to generate.
`centerline`	the centerline of the distribution, represented as a one- dimensional data structure of length P containing the measurement of the centerline on grid points.
`Cov`	the covariance operator (provided in form of a P x P matrix) that has to be used in the generation of ε(t). At least one argument between `Cov` and `CholCov` should be different from `NULL`.
`CholCov`	the Cholesky factor of the covariance operator (provided in form of a P x P matrix) that has to be used in the generation of observations from the process ε(t). At least one argument between `Cov` and `CholCov` should be different from `NULL`.

In particular, the following model is considered for the generation of data:

X(t) = m( t ) + ε(t), for all t in I = [a, b]

where m(t) is the center and ε(t) is a centered gaussian process with covariance function C_i. That is to say:

Cov( ε(s), ε(t) ) = C( s, t ), with s, t in I

All the functions are supposed to be observed on an evenly-spaced, one- dimensional grid of P points: [a = t_0, t_1, …, t_{P-1} = b] \subset I .

The function returns a matrix containing the discretized values of the generated observations (in form of an N x P matrix).

exp_cov_function, fData, generate_gauss_mfdata

N = 30
P = 1e2

t0 = 0
tP = 1

time_grid = seq( t0, tP, length.out = P )

C = exp_cov_function( time_grid, alpha = 0.1, beta = 0.2 )

CholC = chol( C )

centerline = sin( 2 * pi * time_grid )

invisible(generate_gauss_fdata( N, centerline, Cov = C ))

invisible(generate_gauss_fdata( N, centerline, CholCov = CholC ))