Related papers: Random Flag Complexes and Asymptotic Syzygies
Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…
For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
In this Note we introduce a new methodology for Bayesian inference through the use of $\phi$-divergences and the duality technique. The asymptotic laws of the estimates are established.
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
This letter presents new nontrivial stochastic identities for random isotropic second rank tensor fields. They can be considered as markers of statistical isotropy in turbulent flows of any nature. The case of axial symmetry is also…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…
In order to physically enlighten the relationship between {\it $q$--independence} and {\it scale-invariance}, we introduce three types of asymptotically scale-invariant probabilistic models with binary random variables, namely (i) a family,…
We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…
The framework of trans-Planckian asymptotic safety has been shown to generate phenomenological predictions in the Standard Model and in some of its simple new physics extensions. A heuristic approach is often adopted, which bypasses the…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.
We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t =…
Starting from Montgomery's conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of L-functions. In particular, moments of characteristic polynomials of random matrices have been…