GetGCVbw2D {KFPCA}

Bandwidth selection through GCV for two-dimension cases

Description

Bandwidth selection through generalized cross-validation (GCV) for two-dimension cases.

Usage

GetGCVbw2D(tPairs, yin, Lt, kern, ObsGrid, RegGrid, dataType = "Sparse")

Arguments

tPairs

A matrix with two columns containing the pairs of time points.

yin

A vector denoting the corresponding values.

Lt

A list of n vectors, where n is the sample size. Each entry contains the observation time in ascending order for each subject.

kern

A character denoting the kernel type; 'epan'(Epanechnikov), 'unif'(Uniform), 'quar'(Quartic), 'gauss'(Gaussian).

ObsGrid

A vector containing all observation grids in ascending order.

RegGrid

A vector of the equally spaced time points in the support interval.

dataType

A character denoting the data type; 'Sparse'-default, 'Dense'.

Value

A scalar denoting the optimal bandwidth.

Examples

# Generate data
n <- 100
interval <- c(0, 10)
lambda_1 <- 9 #the first eigenvalue
lambda_2 <- 1.5 #the second eigenvalue
eigfun <- list()
eigfun[[1]] <- function(x){cos(pi * x/10)/sqrt(5)}
eigfun[[2]] <- function(x){sin(pi * x/10)/sqrt(5)}
score <- cbind(rnorm(n, 0, sqrt(lambda_1)), rnorm(n, 0, sqrt(lambda_2)))
DataNew <- GenDataKL(n, interval = interval, sparse = 6:8, regular = FALSE,
                     meanfun = function(x){0}, score = score,
                     eigfun = eigfun, sd = sqrt(0.1))
# Optimal bandwidth for the estimate of
# E{X(s)X(t)} = cov(X(s), X(t)) + mu(s) * mu(t)
xin2D <- NULL
yin2D <- NULL
for(i in 1:n){
  xin2D <- rbind(xin2D, t(utils::combn(DataNew$Lt[[i]], 2)))
  yin2D <- rbind(yin2D, t(utils::combn(DataNew$Ly[[i]], 2)))
}
tPairs <- xin2D
yin <- yin2D[,1] * yin2D[, 2]
bwOpt <- GetGCVbw2D(tPairs = tPairs, yin = yin, Lt = DataNew$Lt,
                    kern = "epan", ObsGrid = sort(unique(unlist(DataNew$Lt))),
                    RegGrid = seq(interval[1], interval[2], length.out = 51))