I'm trying to calculate the sampling variances for a two-parameter ML problem. My likelihood function is non-standard, and I maximize it using numerical methods. The problem I'm having is estimating the variance of my estimates.
The only reference I can find to this problem (and I'm a newcomer to statistics) is in Kendall & Stuart, vol 2, Chapter 18. After demonstrating that the variances (i.e., the dispersion matrix) can be got from calculating some expectations (18.26) or, if there exist jointly sufficent statistics, by direct substitution of the estimates into the derivatives of the log-likelihood function (18.27). Neither of these methods are practical for my problem. Kendall & Stuart recognize that in most cases, this will be true, for they add (end of 18.27) that "the elements of the dispersion matrix may be estimated from the sample by standard methods."
What are these "Standard Methods"? That seems to be the way I need to go.
Thanks for any insight. Email welcome.
Jeph -- Jeph Herrin, Ph.D. Assistant Professor Emory University Center for Clinical Evaluation Sciences School of Medicine Emory University firstname.lastname@example.org