Computes the distribution of `g(x)` where `x` is an `mle` object.

By the invariance property of the MLE, if `x` is an `mle` object, then under the right conditions, asymptotically, `g(x)` is normally distributed, g(x) ~ normal(g(point(x)),sigma) where `sigma` is the variance-covariance of `f(x)`

Usage

# S3 method for class 'mle'
rmap(x, g, ..., n = 1000, method = c("mc", "delta"))

Arguments

x

an `mle` object

g

a function

...

additional arguments to pass to the `g` function

n

number of samples to take to estimate distribution of `g(x)` if `method == "mc"`.

method

method to use to estimate distribution of `g(x)`, "delta" or "mc".

Value

An mle object of class rmap_mle representing the transformed MLE with variance estimated by the specified method.

Details

We provide two different methods for estimating the variance-covariance of `f(x)`: method = "delta" -> delta method method = "mc" -> monte carlo method

Examples

# MLE for normal distribution
set.seed(123)
x <- rnorm(100, mean = 5, sd = 2)
n <- length(x)
fit <- mle(
  theta.hat = c(mu = mean(x), var = var(x)),
  sigma = diag(c(var(x)/n, 2*var(x)^2/n)),
  nobs = n
)

# Transform: compute MLE of standard deviation (sqrt of variance)
# Using delta method
g <- function(theta) sqrt(theta[2])
sd_mle <- rmap(fit, g, method = "delta")
params(sd_mle)
#> [1] 1.825632
se(sd_mle)
#> [1] 0.1290917