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The Fisher information matrix (in the scalar parameter case) can be obtained from the Kullback-Leibler divergence by

$$g(\theta) = -\frac{\partial}{\partial \theta}\frac{\partial}{\partial \theta'}D(p_\theta\|p_{\theta'})\Bigg|_{\theta'=\theta},$$ where $$D(p_\theta\|p_\theta') = \int p_\theta(x)\log\frac{p_\theta(x)}{p_{\theta'}(x)}.$$

I would like to know if the analogous information matrix in the Bhattacharya bound (the matrix $V_K$) can also be obtained from a divergent function. Any help in this connection is greatly appreciated.

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  • $\begingroup$ please clarify "divergent function". I took it to mean some kind of information divergence. $\endgroup$
    – kodlu
    Commented Jan 28, 2022 at 8:51
  • $\begingroup$ @kodlu: Yes, by a 'divergence function', I mean an information divergence such as 'Kullback_leibler divergence'. However, I would like to derive the information matrix in the Bhattacharya bound from it. $\endgroup$
    – Ashok
    Commented Jan 28, 2022 at 9:45

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