Related papers: Berman's inequality under random scaling
Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information. They satisfy Bell's inequality and exhibit spatial non stationarity in angle. Correlations for three…
We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.
Let $\pa{X_{t}}_{t\in T}$ be a family of real-valued centered random variables indexed by a countable set $T$. In the first part of this paper, we establish exponential bounds for the deviation probabilities of the supremum $Z=\sup_{t\in…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving…
We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
Tur\'an type inequalities for modified Bessel functions of the first kind are used to deduce some sharp lower and upper bounds for the asymptotic order parameter of the stochastic Kuramoto model. Moreover, approximation from the Lagrange…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…