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I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field. I have read (4) and parts of (3). …

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 …

I am firstly an algebraist and later shifted to probability somehow, so I think I can answer your question from my own experience. I am a algebraist from the bottom of my heart though...A natural thou …

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 …

The question is clarified by Prof.V.Vovk. See his answer below for discussion. Recently, early works of Gammerman, Vanpnik and Vovk[4] are rediscovered by Wasserman et.al[1] and proposed it as a promi …

I hope I understood the OP correctly, in case not please let me know. And I will discuss the case of eigenvalue instead of singular value without much loss of generality. In case you are only interes …

There is an excellent issue of Statistical Science that address the James-Stein phenomena from various aspects. https://www.jstor.org/stable/i23208816 Question What does it mean that a James-Stein es …

First of all I have to express my opinion that the gap between large sample behavior and the finite sample behavior should be considered "unsurprising". Basically speaking, the theory of asymptotics …

A possible relevant post What kind of random matrices have rapidly decaying singular values?. In that post I discussed the distribution of maximal eigenvalue of a random matrix based on the result [Jo …

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 …

This question is partially inspired by the following MO post: What are some of the surprising results of finite sample statistical estimation? and current heated research front of high dimensional sta …

The quote actually belongs to C.G.Rota. Because cumulant sequences are closed under addition while moment sequences are not. That makes cumulant a more tractable algebraic structure altogether. Altho …

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 …

The Berry-Essen bound stated that $$\sup _{{x\in {\mathbb R}}}\left|\widehat{F_{n}(x)}-\Phi (x)\right|\leq C_{0}\cdot \psi _{0}$$ where $\psi _{0}(n)={\Big (}{\textstyle \sum \limits _{{i=1}}^{n}\si …

Partly inspired by recent developments in enumeration of pattern avoiding permutations, which is known to be connected with Brownian excursions [Hoffman&Rizzolo]. The exciting milestone is the solutio …