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I`m using the Newton-Raphson method for obtaining MLE for parameters for maximizing my objective function.
At each iteration, I want to check that is the Hessian matrix negative definite or not and I see the Hessian matrix is not negative definite. So, I want to use the Fisher information matrix. I mean
enter image description here
I know the expectation has to be taken w.r.t the true parameters. Is it correct in the Newton-Raphson method that the expectation is taken w.r.t obtained parameters values in previous iteration? In this situation, the Fisher information matrix in above is indefinite!! Is it possible? What are the reasons for this? Are the second-order derivatives wrong? Or are values of expectations incorrect? Thank you.

user321525
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    See [this question](https://stats.stackexchange.com/q/495033/60613) – Firebug Jun 02 '21 at 11:23
  • Does this answer your question? [Why is the observed Fisher information defined as the Hessian of the log-likelihood?](https://stats.stackexchange.com/questions/495033/why-is-the-observed-fisher-information-defined-as-the-hessian-of-the-log-likelih) – mdewey Jun 02 '21 at 13:56
  • @ mdewey I edited my question. Thank you. – user321525 Jun 02 '21 at 14:28

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