toeplitz_estimator <- function(x, k){
p <- ncol(x)
allelements <- c(x)
for(i in 0:(p-1)){
omega <- ifelse(i <= k/2, 1, ifelse(i <= k & i > k/2, 2-2*i/k, 0))
aa <- allelements[seq(1+i, length(allelements) - p*(i-1), by = p + 1)]
allelements[seq(1+i, length(allelements) - p*(i-1), by = p + 1)] <- mean(aa)*omega
allelements[seq(1+p*i, length(allelements), by = p + 1)] <- mean(aa)*omega
}
y <- matrix(allelements, p, p)
return(y)
}
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