FPCscoreLSE {KFPCA}

Least square estimates of functional principal component scores

Description

Least square estimates (LSE) of functional principal component scores.

Usage

FPCscoreLSE(Lt, Ly, kern, bw, FPC_dis, RegGrid, more = FALSE)

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).

bw

A scalar denoting the bandwidth for mean function estimate.

FPC_dis

A nRegGrid by nK matrix containing the eigenfunction estimates at RegGrid, where nRegGrid is the length of RegGrid and nK is the number of FPCs.

RegGrid

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

more

Logical; If FALSE, only the estimates of FPC scores are returned. If TRUE, the mean function estimates and the eigenfunction estimates at all observation time points are also returned.

Value

If more = FALSE, a n by nK matrix containing the estimates of the FPC scores is returned, where n is the sample size. If more = TRUE, a list containing the following components is returned:

score

a n by nK matrix containing the estimates of the FPC scores.

meanest_fine

Mean function estimates at all observation time points.

FPC_dis_fine

Eigenfunction estimates at all observation time points.

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 = 3:5, regular = FALSE,
                     meanfun = function(x){0}, score = score,
                     eigfun = eigfun, sd = sqrt(0.1))
basis <- fda::create.bspline.basis(interval, nbasis = 13, norder = 4,
                              breaks = seq(0, 10, length.out = 11))
Klist <- KFPCA(DataNew$Lt, DataNew$Ly, interval, nK = 2, bw = 1,
               nRegGrid = 51, fdParobj = basis)
# Just an example to explain the use of FPCscoreLSE().
# One can obtain FPC scores estimates for KFPCA method
# by KFPCA() directly. Note that FPCscoreLSE() can also be used
# to estimate FPC scores for methods except KFPCA.
scoreKFPCA <- FPCscoreLSE(DataNew$Lt, DataNew$Ly, kern = "epan",
                          bw = Klist$bwmean, FPC_dis = Klist$FPC_dis,
                          RegGrid = seq(interval[1], interval[2], length.out = 51))