Related papers: Studentized Processes of U-statistics
This work initiates a general study of learning and generalization without the i.i.d. assumption, starting from first principles. While the traditional approach to statistical learning theory typically relies on standard assumptions from…
We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and…
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…
In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements…
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are…
Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
We calculate the rate of decrease of the expectation value of the transverse component of spin for spin-1/2 particles in a magnetic field with a spatial gradient, to determine the conditions under which a previous classical description is…
In this work we show that the standard method to obtain nucleation rate-predictions with the aid of atomistic Monte-Carlo simulations leads to nucleation rate predictions that deviate $3-5$ orders of magnitude from the recent brute-force…
In this paper, convergence for moments of powered normal extremes is considered under an optimal choice of normalizing constants. It is shown that the rates of convergence for normalized powered normal extremes depend on the power index.…
We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Building on work by Tsirelson, we present a family of protocols that detect the nonclassicality of suitable states of a single quantum system, under the sole assumption that the measured dynamical observable undergoes a uniform precession.…
We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential…
We consider the 2-dimensional random matching problem in $\mathbb{R}^2.$ In a challenging paper, Caracciolo et. al. arXiv:1402.6993 on the basis of a subtle linearization of the Monge Ampere equation, conjectured that the expected value of…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…
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…
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…