Related papers: The Independence under Sublinear Expectations

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…

A rational probability distribution on four binary random variables $X, Y, Z, U$ is constructed which satisfies the conditional independence relations $[X \mathrel{\text{$\perp\mkern-10mu\perp$}} Y]$, $[X…

Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution…

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…

In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…

A short, information-theoretic proof of the Kac--Bernstein theorem, which is stated as follows, is presented: For any independent random variables $X$ and $Y$, if $X+Y$ and $X-Y$ are independent, then $X$ and $Y$ are normally distributed.

In this study, we propose the sublinear expectation structure under countable state space. To describe an interesting "nonlinear randomized" trial, based on a convex compact domain, we introduce a family of probability measures under…

Inference of the conditional dependence structure is challenging when many covariates are present. In numerous applications, only a low-dimensional projection of the covariates influences the conditional distribution. The smallest subspace…

It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…

In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal…

We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…

In this investigation, the distribution of the ratio of two independently distributed xgamma (Sen et al. 2016) random variables X and Y , with different parameters, is proposed and studied. The related distributional properties such as,…

The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely…

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…