Related papers: Non-asymptotic estimation for Bell function, with …

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 introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…

We consider estimation in a particular semiparametric regression model for the mean of a counting process with ``panel count'' data. The basic model assumption is that the conditional mean function of the counting process is of the form…

Generalizing the well-known mean-value property of harmonic functions, we prove that a p-harmonic function of two variables satisfies, in a viscosity sense, two asymptotic formulas involving its local statistics. Moreover, we show that…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main…

A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…

Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these…

We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust…

We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.

In this paper, we study mixed power-exponential moment functionals of nonlinearly perturbed semi-Markov processes in discrete time. Conditions under which the moment functionals of interest can be expanded in asymptotic power series with…

The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…

The Probability Estimation Framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum non-locality…

This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…

The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…