What are some strategies for estimating the variance of a statistic that is an arbitrary function of multiple random variables? I am familiar with the Delta method which uses asymptotics to estimate the variance of a statistic when the function takes a single random variable as its input (e.g. $g(X) = log(X)$). But what are methods for when the statistic involves two or three random variables, such as:
$g(X,Y,Z) = log(X+Z)-log(Y+Z)$
Note in this case the random variables are i.i.d binomials whose mean and variance I have estimated from count data.