Functional Cross Covariance between longitudinal variable Y and longitudinal variable X
Calculate the raw and the smoothed cross-covariance between functional predictors using bandwidth bw or estimate that bw using GCV.
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" )
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 |
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 |
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
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)
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