Returns the limiting distribution of √n(g(ˉXn)−g(μ)) under the Delta Method. For a univariate distribution, this is N(0,g′(μ)2σ2). For a multivariate distribution with Jacobian J=Dg(μ), this is MVN(0,JΣJT).
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