Related papers: Higher Dimensional Quasi-Power Theorem and Berry-E…

We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension $D$ to increase with the…

New Berry--Esseen-type bounds, with explicit constant factors, for the distribution of the Student statistic and, equivalently, for that of the self-normalized sum of independent zero-mean random variables are obtained. These bounds are…

We show, how the classical Berry-Esseen theorem for normal approximation may be used to derive rates of convergence for random sums of centerd, real-valued random variables with respect to a certain class of probability metrics, including…

Supersymmetric gauge theories in four dimensions can display interesting non-perturbative phenomena. Although the superpotential dynamically generated by these phenomena can be highly nontrivial, it can often be exactly determined. We…

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…

This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random…

We show that, under certain assumptions, the fitness of almost all quasi-species becomes independent of mutational probabilities and the initial frequency distributions of the sequences in high dimensional sequence spaces. This result is…

In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order…

Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…

Let F : W --> V be a dominant rational map between quasi-projective varieties of the same dimension. We give two proofs that h_V(F(P)) >> h_W(P) for all points P in a nonempty Zariski open subset of W. For dominant rational maps F : P^n -->…

We consider approximation properties of real points by uniformly distributed sequences. Under some assumptions on the approximation functions, we prove a Khintchine-type $0$-$1$ dichotomy law. We establish a new connection between uniform…

It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way,…

Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the…

The BK inequality (\cite{BK85}) says that,for product measures on $\{0,1\}^n$, the probability that two increasing events $A$ and $B$ `occur disjointly' is at most the product of the two individual probabilities. The conjecture in…

We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used…

In this paper, we propose a simple inferential method for a wide class of panel data models with a focus on such cases that have both serial correlation and cross-sectional dependence. In order to establish an asymptotic theory to support…

We present a generalized quasi-particle theory for bosonic lattice systems, which naturally contains all relevant collective modes, including the Higgs amplitude in the strongly correlated superfluid. In contrast to Bogoliubov theory, this…

The Equidistribution Conjecture is proved for general semiabelian varieties over number fields. Previously, this conjecture was only known in the special case of almost split semiabelian varieties through work of Chambert-Loir. The general…

We consider nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes…