Least square estimates of functional principal component scores
Least square estimates (LSE) of functional principal component scores.
FPCscoreLSE(Lt, Ly, kern, bw, FPC_dis, RegGrid, more = FALSE)
Lt |
A |
Ly |
A |
kern |
A |
bw |
A scalar denoting the bandwidth for mean function estimate. |
FPC_dis |
A |
RegGrid |
A |
more |
Logical; If |
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 |
meanest_fine |
Mean function estimates at all observation time points. |
FPC_dis_fine |
Eigenfunction estimates at all observation time points. |
# 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, 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))
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