Is mathematical statistics an active area of research? Are there big unsolved problems in the area? I am interested in seeing areas of mathematical statistics where there is active research. For example in pure math algebraic number theory, analytic number theory, analytic combinatorics etc etc are all active areas with lots of research. I was wondering if mathematical statistics is such an area and what are the active topics of research within it.

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    $\begingroup$ Well, if you could generalize the Cramer-Rao bound from a matrix inverse to some sort of k-mode tensor inverse (w/e that would look like as an operator I am unsure) I would be excited. $\endgroup$
    – Galen
    Aug 31, 2023 at 21:11
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    $\begingroup$ Mathematical Statistics as a field is quite expansive. Is there any topic within Mathematical Statistics that you're "looking at"? If there is, I think you'd better luck getting an answer. $\endgroup$
    – Jxson99
    Aug 31, 2023 at 21:28
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    $\begingroup$ This is the kind of broad question that could be greatly improved through some initial research. See, for instance, imstat.org. $\endgroup$
    – whuber
    Aug 31, 2023 at 21:36
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    $\begingroup$ Aren't JASA and the Annals of Statistics pretty into mathematical statistics? Perhaps try looking through their recent articles instead of Google. $\endgroup$
    – Dave
    Aug 31, 2023 at 22:11
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    $\begingroup$ I am quite baffled at even questioning effectively as to whether mathematical statistics is dead. Firstly, it's not a monolithic field. It comprises of so many topics/branches/sub-fields. Of course, one sub-field should be dense with new research and innovation while others are pretty much low to stagnant, probably due to being localized or the development is near to completion. A mathematical statistician doesn't delve into the whole mathematical statistics. Rather they choose a one or two topics and try to steer through ahead. Find yours and see the latest research there. $\endgroup$ Sep 1, 2023 at 2:12