GetCrCovYX {fdapace}

Functional Cross Covariance between longitudinal variable Y and longitudinal variable X

Description

Calculate the raw and the smoothed cross-covariance between functional predictors using bandwidth bw or estimate that bw using GCV.

Usage

GetCrCovYX(
  bw1 = NULL,
  bw2 = NULL,
  Ly1,
  Lt1 = NULL,
  Ymu1 = NULL,
  Ly2,
  Lt2 = NULL,
  Ymu2 = NULL,
  useGAM = FALSE,
  rmDiag = FALSE,
  kern = "gauss",
  bwRoutine = "l-bfgs-b"
)

Arguments

bw1

Scalar bandwidth for smoothing the cross-covariance function (if NULL it will be automatically estimated) (Y)

bw2

Scalar bandwidth for smoothing the cross-covariance function (if NULL it will be automatically estimated) (X)

Ly1

List of N vectors with amplitude information (Y)

Lt1

List of N vectors with timing information (Y)

Ymu1

Vector Q-1 Vector of length nObsGrid containing the mean function estimate (Y)

Ly2

List of N vectors with amplitude information (X)

Lt2

List of N vectors with timing information (X)

Ymu2

Vector Q-1 Vector of length nObsGrid containing the mean function estimate (X)

useGAM

Indicator to use gam smoothing instead of local-linear smoothing (semi-parametric option) (default: FALSE)

rmDiag

Indicator to remove the diagonal element when smoothing (default: FALSE)

kern

String specifying the kernel type (default: FALSE; see ?FPCA for details)

bwRoutine

String specifying the routine used to find the optimal bandwidth 'grid-search', 'bobyqa', 'l-bfgs-b' (default: 'l-bfgs-b') If the variables Ly1 and Ly2 are in matrix form the data are assumed dense and only the raw cross-covariance is returned. One can obtain Ymu1 and Ymu2 from FPCA and ConvertSupport.

Value

A list containing:

smoothedCC

The smoothed cross-covariance as a matrix (currently only 51 by 51)

rawCC

The raw cross-covariance as a list

bw

The bandwidth used for smoothing as a vector of length 2

score

The GCV score associated with the scalar used

smoothGrid

The grid over which the smoothed cross-covariance is evaluated

References

Yang, Wenjing, Hans-Georg Müller, and Ulrich Stadtmüller. "Functional singular component analysis." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73.3 (2011): 303-324

Examples

Ly1= list( rep(2.1,7), rep(2.1,3),2.1 );
Lt1 = list(1:7,1:3, 1);
Ly2 = list( rep(1.1,7), rep(1.1,3),1.1); 
Lt2 = list(1:7,1:3, 1);
Ymu1 = rep(55,7);
Ymu2 = rep(1.1,7);
AA<-GetCrCovYX(Ly1 = Ly1, Ly2= Ly2, Lt1=Lt1, Lt2=Lt2, Ymu1=Ymu1, Ymu2=Ymu2)