How important is real analysis to statistics?

How important is real analysis to statistics?


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Quote:

Originally Posted by quora contributor Statistical theory deals with convergence of sequences of random variables in high-dimensional Euclidean spaces. How could you not need real analysis to think about that? That's not to say that you need that sort of background to use statistical methods. But if you want to understand the methods and their limitations at anything more than a superficial level, you need to be able to connect with the theory. And I have to admit, the idea that you can study a non-trivial amount of optimization without real analysis is somewhat amusing.

How important is real analysis to statistics?