Numerical aproximation of the Hessian of a function.
hessian(f, x0, ...)(type: numeric) name of function that defines log likelihood (or negative of it).
(type: numeric) scalar or vector of parameters that give the point at which you want the hessian estimated (usually will be the mle).
Additional arguments to be passed to the function.
An \(n \times n\) matrix of 2nd derivatives, where \(n\) is the length of
x0.
Computes the numerical approximation of the Hessian of f, evaluated at
x0.
Usually needs to pass additional parameters (e.g. data). N.B. this uses no
numerical sophistication.
# Variance of the maximum likelihood estimator for mu parameter in
# gaussian data
loglik <- function(series, x, sd = 1) {
-sum(log(dnorm(series, mean = x, sd = sd)))
}
sqrt(c(var(malleco) / length(malleco), diag(solve(hessian(
f = loglik, x = mean(malleco), series = malleco,
sd = sd(malleco)
)))))
#> [1] 0.00607085 0.00607085