Returns the limiting distribution of \(\sqrt{n}(g(\bar{X}_n) - g(\mu))\) under the Delta Method. For a univariate distribution, this is \(N(0, g'(\mu)^2 \sigma^2)\). For a multivariate distribution with Jacobian \(J = Dg(\mu)\), this is \(MVN(0, J \Sigma J^T)\).
delta_clt(base_dist, g, dg)A dist object representing the base distribution.
The function to apply to the sample mean.
The derivative (univariate) or Jacobian function (multivariate)
of g. For univariate distributions, dg(x) should return
a scalar. For multivariate distributions, dg(x) should return
a matrix (the Jacobian).
A normal or mvn distribution representing the
Delta Method limiting distribution.
# Delta method: g = exp, dg = exp
x <- exponential(rate = 1)
z <- delta_clt(x, g = exp, dg = exp)
mean(z)
#> [1] 0
vcov(z)
#> [1] 7.389056