covfunc: Estimate the cov function from functional data/snippets.

In ZhuolinSong/wpe: Written Preliminary Exam or Literature Review: Methods for Functional Snippets

Estimate the cov function from functional data/snippets.

Description

Estimate the cov function from functional data/snippets.

Usage

covfunc(
  t,
  y,
  newt = NULL,
  mu = NULL,
  weig = NULL,
  method = c("FOURIER", "PACE", "SP"),
  ...
)

Arguments

t	a list of vectors (for irregular design) or a vector (for regular design) containing time points of observations for each individual; each vector should be in ascending order.
y	a list of vectors (for irregular design) or a matrix (for regular design) containing the observed values at t; if it is a matrix, the columns correspond to the time points in the vector t.
newt	a list of vectors or a vector containing time points of observations to be evaluated; if NULL, then newt is treated as t.
mu	the known or estimated mean function object; it must be a scalar (viewed as a constant function), a function handle, or an object obtained by calling meanfunc
weig	a vector of length(t) of weight for each subject, or 'OBS' or 'SUBJ' for weighting scheme
method	estimation method, 'PACE' or 'FOURIER' or 'SP' (for semiparametric method)
...	other parameters required depending on the method and tuning; see details
tuning	tuning method to select possible tuning parameters

Details

• When method='PACE', additional parameters are

  kernel

  kernel type; supported are 'epanechnikov', "rectangular", "triangular", "quartic", "triweight", "tricube", "cosine", "gauss", "logistic", "sigmoid" and "silverman"; see https://en.wikipedia.org/wiki/Kernel_(statistics) for more details.

  deg

  degree of the local polynomial regression; currently only deg=1 is supported.

  bw

  bandwidth

• When method='FOURIER', additional parameters are

  q

  number of basis functions; if NULL then selected by tuning method

  rho

  roughness penalty parameter; if NULL then selected by tuning method

  ext

  extension margin of Fourier extension; if NULL then selected by tuning method

  domain

  time domain; if NULL then estimated by (min(t),max(t))

• When method='SP', additional parameters are

  domain

  time domain; if NULL then estimated by (min(t),max(t))

  corf

  function of the form function(theta,x,y) that specifies the correlation structure with parameter theta; If NULL then Matern correlation is used.

  sig2e

  variance of measurement error; if NULL the automatically calculated by the calling sigma2

  sig2x

  variance function; a function or an object generated by varfunc; if NULL then automatically estimated by calling varfunc

  pfunc

  penalty function on the estimation; Not used yet.

  theta0

  Initial value for the parameter theta to be estimated; NULL by default

  lb

  vector of lower bound of theta; if NULL then set to -Inf for all coordinate

  ub

  vector of upper bound of theta; if NULL then set to Inf for all coordinate

  D

  dimension of theta

Value

an object of the class 'covfunc' containing necessary information to predict/evaluate the estimated covariance function and the following output:

• When method='PACE', additional parameters are

  fitted

  fitted value at the grid spanned by newt

  delta

  the largest span among all subjects; note that it is not normalized by the span of the whole study.

  bw

  selected bandwidth by tuning method if NULL is the input for bw.

  mu

  estimated mean function if NULL is the input.

• When method='FOURIER', additional parameters are

  fitted

  fitted value at the grid spanned by newt

  q

  selected q if NULL is the input

  rho

  selected rho if NULL is the input

  ext

  selected ext if NULL is the input

  C

  estimated coefficients

  mu

  estimated mean function if NULL is the input.

• When method='SP', additional parameters are

  fitted

  fitted value at the grid spanned by newt

  domain

  time domain; if NULL then estimated by (min(t),max(t)).

  rho

  estimated function of the form function(x,y) of the correlation structure.

  sig2e

  estiamted variance of measurement error if NULL is the input.

  sig2x

  estiamted variance function if NULL is the input.

  theta

  estimated parameters for the correlation structure.

  mu

  estimated mean function if NULL is the input.

References

\insertRef

Lin2020bmcfda

\insertRef

Lin2020mcfda

\insertRef

Yao2005mcfda

Examples

mu <- function(s) sin(2*pi*s)
D <- synfd::sparse.fd(mu=mu, X=synfd::gaussian.process(), n=100, m=5)
mu.obj <- meanfunc(D$t,D$y,newt=NULL,method='PACE',
                   tuning='cv',weig=NULL,kernel='gauss',deg=1)
cov.obj <- covfunc(D$t,D$y,newt=NULL,mu=mu.obj,method='FOURIER',
                   tuning='cv',weig=NULL,domain=c(0,1))
cov.hat <- predict(cov.obj,regular.grid())

ZhuolinSong/wpe documentation built on Oct. 31, 2022, 7:38 p.m.