GetGCVbw1D {KFPCA}

Bandwidth selection through GCV for one-dimension cases

Description

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

Usage

GetGCVbw1D(Lt, Ly, kern, dataType = "Sparse")

Arguments

Lt

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

Ly

A list of n vectors, where n is the sample size. Each entry contains the measurements of each subject at the observation time correspond to Lt.

kern

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

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 mean function estimate
bwOpt <- GetGCVbw1D(DataNew$Lt, DataNew$Ly, kern = "epan")