irreg.fd: Sample Irregular Functional Data
In synfd: Synthesize Dense or Sparse Functional Data/Snippets

Description Usage Arguments Details Value References Examples

Sample Irregular Functional Data

irreg.fd(
  mu = 0,
  X = wiener.process(),
  n = 100,
  m = 5,
  sig = NULL,
  snr = 5,
  domain = c(0, 1),
  delta = 1
)

`mu`	function, scalar or a vector defining the mean function; default value: `0`.
`X`	centered stochastic process defined by a function of the form `X(tObs,n)` and returning `n*length(tObs)` matrix, where each row represents observations from a trajectory. Default value: `wiener.process()`.
`n`	sample size; default value: `100`.
`m`	a vector of sampling rate or scalar of average sampling rate or a function of the form `f(n)` generating `n` positive integers; default value: `5`.
`sig`	standard deviation of measurement errors; if `NULL` then determined by `snr`.
`snr`	signal to noise ratio to determine `sig`; default value: `5`.
`domain`	the domain; default value: `c(0,1)`.
`delta`	the proportion of the domain to be observed for each trajectory; default value: `1`.

The number of observation for each trajectory is randomly generated by rpois(m)+1. For each trajectory, the reference time Oi is uniformly sampled from the interval [domain[1]+delta*L/2,domain[2]-delta*L/2], where L is the length of domain, and the design points for the trajectory is uniformly sampled from the interval [Oi-delta*L/2,Oi+delta*L/2].

a list with the following members

t: list of design points sorted in increasing order for each trajectory.
y: list of vectors of observations for each trajectory.

and with attributes sig, snr, domain, delta and

y0: n*m matrix of observations without measurement errors.

\insertRef

Lin2020synfd

# Gaussian trajectories with constant mean function 1
Y <- irreg.fd(mu=1, X=gaussian.process(), n=10, m=5)

# trajectories froma a process defined via K-L representation
Y <- irreg.fd(mu=cos, X=kl.process(eigen.functions='FOURIER',distribution='LAPLACE'),n=10, m=5)

# trajectories with specified individual sampling rate
Y <- irreg.fd(mu=1, X=gaussian.process(cov=matern), n=10, m=rpois(10,3)+2)