## The population mean.
mu = 1

## The sample size.
n = 10

## The number of simulation replications.
nrep = 1e3

Q = array(0, c(nrep,3))

for (k in 1:1e3) {

    ## Generate the logistic data.
    U = runif(n)
    Y = mu + log(U/(1-U))

    ## Starting value.
    m = mean(Y)

    ## Newton's method.
    while (TRUE) {

        V = exp(-(Y-m))

        ## The first derivative of the log-likelihood.
        D1 = n - 2*sum(V/(1+V))

        ## Check for convergence.
        if (abs(D1) < 1e-10) { break }

        ## The second derivative of the log-likelihood.
        D2 = -2*sum(V/(1+V)^2)

        ## Newton's step.
        m = m - D1/D2
    }

    ## The approximate standard error.
    SE = sqrt(-1/D2)

    Q[k,] = c(m, SE, 1*(abs(m-mu) < 2*SE))
}