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Are you trying to construct an infinite-dimensional (Hilbert) manifold of probability measures on a fixed measurable space? Or you simply want to find a Bergman divergence analog in order to generaliz …

@Carlo's answer is very insightful from a physics perspective, thanks a lot for the teaching and learning here. My answer is from a more ML and statistic perspective as @Ed Smith asked. But in the OP, …

I may start answering by pointing out that the term "nonparametrics statistics" is essentially "parametric". The existing methods (e.g. Smoothing splines) in nonparametrics, are somehow all parametriz …

I think it is just called (scaled) supremum $L_1$ norm and it is mostly studied in Bayesian nonparametric estimation literature, especially posterior consistency. The following paper investigate condi …

It has been recently mentioned by a speaker (his talk is completely not relevant to random matrix theory/RMT though) that modern statistics, especially random matrices theory, will help solving some n …

Iosif Pinelis provided a very nice answer, however, I would like to provide a more comprehensive answer to this question. I think the title is a bit misleading because we do not actually need the orde …

Non-Gaussianness is an ambiguous concept. In the continuum of probability distributions such as the uniform, where all events are clustered into a given range and equally likely. On the other s …

Note that the Laguerre orthogonal polynomials are in form of [1](bearing combinatoric interpretation) and [3] \begin{align} & L_n^\nu(x)=(-1)^n\sum_{m=0}^n \binom n m \prod_{i=1}^m (\nu+2(n-i))(-x)^{ …

No. Vector space structure is not enough, we actually need a compatible lattice structure to make things work. To apply the conditional expectation operator $E(\bullet\mid Y)$ onto the Hilbert space c …

(1) supported on half planes of $\mathbb{R}^n$, you may want to look at folded Gaussian distributions. (2) supported on a compact surface like $\mathbb{S}^n$, you may want to look at projected Gaussi …

If the process you concern is a harmonizable process then Bochner Theorem can be easily generalized into discrete time case by regarding it as Fourier representation. And in some more specific cases D …

In response to the critical comments below I revised my answer. Hope this is more helpful! (1) Two kinds of metrics are defined on generally different spaces. It is not fair to compare these two met …

You need a global convexity to enjoy the optimal convergence rate, otherwise even local convexity will almost surely(not in probabilistic sense) lead to the worst rate you pointed out. MCMC(Markov Ch …

The answer is yes. Stein operator is essentially no more than a differential equation $E$(written as an operator notation) which characterized a distribution $f$ as its unique solution. That is the re …

A thorough discussion is contained in Finch, P. D. "On the covariance determinants of moving-average and autoregressive models." Biometrika 47.1/2 (1960): 194-196. JSTOR But it is more common …