mcfda: Mean and Covariance Estimation for Functional Data Analysis

Description Usage Arguments Details Value References Examples

Estimate the cov function from functional data/snippets.

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

`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

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

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.

\insertRef

Lin2020bmcfda

\insertRef

Lin2020mcfda

\insertRef

Yao2005mcfda

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())