Related papers: Studentized Processes of U-statistics
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $\pi^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to…
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…
We analyse the asymptotic behaviour of the probability of observing the expected number of successes at each stage of a sequence of nested Bernoulli trials. Our motivation is the attempt to give a genuinely frequentist interpretation to the…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
We collect, scattered through literature, as well as we prove some new properties of two Markov processes that in many ways resemble Wiener and Ornstein--Uhlenbeck processes. Although processes considered in this paper were defined either…
We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a perturbation of the classical rule for the…
Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…
We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…
This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being…
Prior research has shown that physics students often think about experimental procedures and data analysis very differently from experts. One key framework for analyzing student thinking has found that student thinking is more point-like,…
A random sampling function Sample:U->{0,1} for a key universe U is a distinguisher with probability p if for any given assignment of values v(x) to the keys x in U, including at least one non-zero v(x)!=0, the sampled sum sum{ v(x) | x in U…
A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been…