fdapace (version 0.1.1)

GetCrCovYZ: Functional Cross Covariance between longitudinal variable Y and scalar variable Z

Description

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

Usage

GetCrCovYZ(bw = NULL, Z, Zmu = NULL, Ly, Lt = NULL, Ymu = NULL,
  support = NULL)

Arguments

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 automaticall 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 (You can get that from FPCA)

support

Vector of unique and sorted values for the support of the smoothed cross-covariance function (if NULL it will be automatically estimated) If the variables Ly1 is in matrix form the data are assumed dense and only the raw cross-covariance is returned.

Value

• A list containing:
• smoothedCC
  The smoothed cross-covariance as a vector
• rawCC
  The raw cross-covariance as a vector
• bw
  The bandwidth used for smoohting as a scaler
• score
  The GCV score associated with the scalar used

References

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

Examples

yList <- list( runif(5),  c(1:3), c(2:4), c(4))
tList <- 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=yList, Lt=tList, Ymu=rep(4,5))