Functional Cross Covariance between longitudinal variable Y and scalar variable Z
Calculate the raw and the smoothed cross-covariance between functional and scalar predictors using bandwidth bw or estimate that bw using GCV
GetCrCovYZ( bw = NULL, Z, Zmu = NULL, Ly, Lt = NULL, Ymu = NULL, support = NULL, kern = "gauss" )
bw |
Scalar bandwidth for smoothing the cross-covariance function (if NULL it will be automatically estimated) |
Z |
Vector N-1 Vector of length N with the scalar function values |
Zmu |
Scalar with the mean of Z (if NULL it will be automatically estimated) |
Ly |
List of N vectors with amplitude information |
Lt |
List of N vectors with timing information |
Ymu |
Vector Q-1 Vector of length nObsGrid containing the mean function estimate |
support |
Vector of unique and sorted values for the support of the smoothed cross-covariance function (if NULL it will be automatically estimated) |
kern |
Kernel type to be used. See ?FPCA for more details. (default: 'gauss')
If the variables Ly1 is in matrix form the data are assumed dense and only
the raw cross-covariance is returned. One can obtain Ymu1
from |
A list containing:
smoothedCC |
The smoothed cross-covariance as a vector |
rawCC |
The raw cross-covariance as a vector |
bw |
The bandwidth used for smoothing as a scalar |
score |
The GCV score associated with the scalar used |
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
Ly <- list( runif(5), c(1:3), c(2:4), c(4)) Lt <- list( c(1:5), c(1:3), c(1:3), 4) Z = rep(4,4) # Constant vector so the covariance has to be zero. sccObj = GetCrCovYZ(bw=1, Z= Z, Ly=Ly, Lt=Lt, Ymu=rep(4,5))
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