fChange (version 2.1.0)

generate_karhunen_loeve: Generate functional data

Description

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
)

Value

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

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.

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)