Generate functional data

generate_karhunen_loeve generates functional data via an autoregressive Karhunen-Loeve expansion. The approach easily accomondate change points in the mean, distribution, eigenvalues, eigenfunctions, and so forth. In a sense, the function creates m `groups' of discretely observed functions with similar properties.

Usage

generate_karhunen_loeve(
  Ns,
  eigenvalues,
  basis,
  means,
  distribution,
  fparam,
  dependence = 0,
  burnin = 100,
  silent = TRUE,
  dof = NULL,
  shape = NULL,
  prev_eps = NULL
)

Arguments

Ns

Vector of Numerics. Each value in Ns is the number of observations for a given group, for m groups.

eigenvalues

Vector of eigenvalues, length 1 or m.

basis

A list of bases (eigenfunctions), length m.

means

A vector of means, length 1 or Ns.

distribution

A vector of distributions, length 1 or m.

fparam

A vector of points indicating the points to evaluate the functions on.

dependence

Numeric [0,1] indicating strength of VAR(1) process.

burnin

A numeric value indicating the number of burnin trials.

silent

A Boolean that toggles displaying the running status.

dof

Numeric for shape with gamma distribution (rate is set to 1).

shape

Numeric for degrees of freedom with t-distribution.

prev_eps

Previous epsilon for dependence across groups. This is only needed if a separate code was run but the new data should be appended. In general only used in internal functions.

Value

List with (1) dfts data and (2) the errors of the last iteration.

Examples

dat1 <- generate_karhunen_loeve(
  Ns=100, eigenvalues=c(1/(1:3)), basis=fda::create.bspline.basis(nbasis=3,norder=3),
  means=0, distribution='Normal',
  fparam=seq(0,1,0.1), dependence=0, burnin=100, silent=TRUE, dof=NULL, shape=NULL,
  prev_eps=NULL)
dat2 <- generate_karhunen_loeve(
  Ns=50, eigenvalues=c(1/(1:4)), basis=fda::create.bspline.basis(nbasis=4),
  means=5, distribution='exponential',
  fparam=seq(0,1,0.1), dependence=0, burnin=100, silent=TRUE, dof=NULL, shape=NULL,
  prev_eps=dat1$prev_eps)

dat <- dfts(cbind(dat1$data$data, dat2$data$data),fparam = dat1$data$fparam)