I am doing a PhD in functional analysis, particularly Banach space theory. Thinking of my future prospect, I would like to venture myself into statistics.
However, as I do not want to 'waste' my background, I would like to search for statistics or machine learning which requires functional analysis to understand its underlying concepts.
I found Bickel et al. Efficient and Adaptive Estimation for Semiparametric Models, Tsiatis's Semiparametric Theory and Missing Data and Small et al. Hilbert Space Methods in Probability and Statistical Inference.
Note that I know functional analysis is required for stochastic calculus, theoretical probability, browninan motion, etc. But I am more interested in statistics.
I also found that similar question was posted reddit.
It would be good if someone can suggest some statistics books that require functional analysis background.