standard error of a correlated sample

stderrcorrelated.R

# Return start of xs as long as f evaluates to TRUE
TakeWhile <-
function(f, x, nomatch = NULL)
{
    pos = Position(Negate(f), x, nomatch = 0L)
    if (pos == 0L) {
        ## f is TRUE everywhere
        if (length(x) > 0L)
            x
        else
            nomatch
    } else if (pos == 1L) {
        ## f is FALSE at first position
        nomatch
    } else {
        ## f is FALSE at some position > 1
        x[1L:(pos - 1L)]
    }
}

# Calculate standard error on a correlated sample
StdErrCorrelated <-
function(x) {
    n = length(x)
    # summing autocorrelations is error prone
    # because we might be summing a lot of values very close to zero
    # negative values are most problematic because we must take square root
    # so as a very rough but always working approximation
    # we sum the first non-negative elements
    # under most circumstances, this gives a conservative approximation
    # of the actual error
    a = TakeWhile(
        function(t) {t>0},
        # do not go further than one 5th of sample
        # see http://w3eos.whoi.edu/12.747/notes/lect06/l06s02.html
        acf(x, plot=FALSE, type="covariance", lag.max=n %/% 5)$acf
        )
    1.96 * sqrt((2 * sum(a) - a[1]) / n)
}