decon_err_het_replicates <- function(xx, W1, W2,deno_U, kernel_type, h, rescale) {
kernel_list <- kernel(kernel_type)
tt <- kernel_list$tt
deltat <- tt[2] - tt[1]
phiK <- kernel_list$phik
OO_sum <- outer(tt / h, (W1 + W2)/2)
num <- rowSums(exp(1i*OO_sum))
den <- deno_U(tt / h)
phi_X <- num/den
rehatphiX <- Re(phi_X)
imhatphiX <- Im(phi_X)
# Matrix of size length(t) x length(xx)
xt <- outer(tt / h, xx)
longx <- length(xx)
# Compute the DKDE estimator
fXdecUK <- cos(xt) * kronecker(matrix(1, 1, longx), rehatphiX) + sin(xt) *
kronecker(matrix(1, 1, longx), imhatphiX)
fXdecUK <- apply(fXdecUK * kronecker(matrix(1, 1, longx), phiK(tt)), 2, sum) /
(2 * pi) * deltat / h
fXdecUK[which(fXdecUK < 0)] <- 0
if (rescale == 1){
dx <- xx[2] - xx[1]
fXdecUK <- fXdecUK / sum(fXdecUK) / dx
}
fXdecUK
}
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