Calculate Two-Sided Hessian Approximation
Calculates an approximation to the Hessian of a function. Used for obtaining an approximation to the information matrix for maximum likelihood estimation.
tsHessian(param, fun, ...)
param |
Numeric. The Hessian is to be evaluated at this point. |
fun |
A function of the parameters specified by |
... |
Values of other parameters of the function |
As a typical statistical application, the function fun is the
log-likelihood function, param specifies the maximum likelihood
estimates of the parameters of the distribution, and the data
constitutes the other parameter values required for determination of
the log-likelihood function.
The approximate Hessian matrix of the function fun where
differentiation is with respect to the vector of parameters
param at the point given by the vector param.
This code was borrowed from the fBasics function, in the file ‘utils-hessian.R’ with slight modification. This was in turn borrowed from Kevin Sheppard's Matlab garch toolbox as implemented by Alexios Ghalanos in his rgarch package.
David Scott d.scott@auckland.ac.nz, Christine Yang Dong c.dong@auckland.ac.nz
hyperbHessian and summary.hyperbFit in
GeneralizedHyperbolic.
### Consider Hessian of log(1 + x + 2y)
### Example from Lang: A Second Course in Calculus, p.74
fun <- function(param){
x <- param[1]
y <- param[2]
return(log(1 + x + 2*y))
}
### True value of Hessian at (0,0)
trueHessian <- matrix( c(-1,-2,
-2,-4), byrow = 2, nrow = 2)
trueHessian
### Value from tsHessian
approxHessian <- tsHessian(c(0,0), fun = fun)
approxHessian
maxDiff <- max(abs(trueHessian - approxHessian))
### Should be approximately 0.045
maxDiffPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.