#' Profiled eta
#' @param y Matrix n by p
#' @export
profiledEta <- function( y ){
n <- nrow(y)
p <- ncol(y)
past <- p*(p+1)/2
sv <- startValues.slash( y )
stopifnot( sv$eta0ml < 0.5 )
Omega <- OmegaMat(sv$Sigma0, sv$eta0ml)
Info <- infoFisher.slash( y, sv$mu0, sv$Sigma0, sv$eta0ml, block = FALSE )
Fetaeta <- Info[p + past + 1, p + past + 1]
Fetagamma <- Info[p + past + 1, 1:(p+past)]
sigma2eta <- c(1/Fetaeta + 1/Fetaeta^2 * t(Fetagamma) %*% Omega %*% Fetagamma)
se <- sqrt(sigma2eta / n )
list( eta=sv$eta0ml, se=se)
}
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