quality of the bhhh-estimator in certain regions

[Yohan]

Hello,

how good is the bhhh-estimator (outer product of the gradient) of the hessian, when the starting value is located within a region of a turning point, where the log-likelihood-function switches from convex to concave (i assume the log-likelihood-function is not globally concave)?
In univariate analysis, the second derivative on such a turning point is zero, whereas the product of the first derivatives has a high value.
Is the bhhh-estimator in such situations a viable approximation to the hessian?

Thank you for your anwers.

Goodbye, Yohan.