rfd: Sample Functional Data

In synfd: Synthesize Dense or Sparse Functional Data/Snippets

Description

Sample Functional Data

Usage

rfd(
  mu = 0,
  X = wiener.process(),
  n = 100,
  m = 5,
  sig = NULL,
  snr = 5,
  domain = c(0, 1),
  delta = 1,
  grid = seq(domain[1], domain[2], length.out = m),
  type = "irregular"
)

Arguments

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	average sampling rate; 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; only required when type="irregular"; default value: 1.
grid	vector of design points; only required when type="regular". default value: NULL.
type	the data type, either "regular" or "irregular"; default value: "irregular".

Details

This is a unified interface for reg.fd and irreg.fd; see the manual for these functions for details.

Value

a list with the following members

t

design points sorted in increasing order for each trajectory; if type="irregular" then a list; otherwise a vector.

y

observations for each trajectory; if type="irregular" then a list; otherwise, a matrix.

and with attributes sig, snr, domain, delta, grid and

y0

the measurement-error-free counterpart of y.

References

\insertRef

Lin2020synfd

Examples

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

# regularly observed trajectories with a K-L representation
Y <- rfd(X=kl.process(eigen.functions='FOURIER',distribution='LAPLACE'), type='regular')

synfd documentation built on July 1, 2020, 6:04 p.m.