CODEWITHSUNDEEP
roptimizationstatisticsmle
jerry
jerry

Reputation: 11

In numerical optimizing likelihood function with R, minimum is achieved, but the hessian matrix is not positive semi-definite

Recently, I have constructed a stats model with the negative log-likelihood to be minimized. There are nine parameters to be estimate (in fact I wanna add two more further). Several optimization method in R have been used,including optim,GenSA, DEoptim,Solnp. Then I got a minimum satisfied.

In the next procedure to compute t-value, it is necessary to compute se:

 sqrt(diag(solve(hessian)))

However, error occurs due to hessian matrix is not positive semi-definite that negative numbers exist in the main diagonal elements. I have tried optimHess or numericHessian to compute different hessian (the hessians are different) but failed all the same. The work suspends.

This question I think is common in multiple parametric statistics. I ask for help that how should I do in this situation.

Upvotes: 1

Views: 980

Answers (1)

datanalytics.com
datanalytics.com

Reputation: 996

There is a paper by Jeff Gill and Gary King discussing this issue. It may help. Essentially, even if theoretically the Hessian should be definite positive at the minimum, because of numerical issues it may not. The paper discusses methods to deal with such matrices.

Upvotes: 2

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