Related papers: Moment bounds for IID sequences under sublinear ex…

In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by…

In Part I of this article (Banerjee and Kuchibhotla (2023)), we have introduced a new method to bound the difference in expectations of an average of independent random vector and the limiting Gaussian random vector using level sets. In the…

Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is…

We consider a sequence of i.i.d. random variables $\{\xi_k\}$under a sublinear expectation $\mathbb{E}=\sup_{P\in\Theta}E_P$. We first give a new proof to the fact that, under each $P\in\Theta$, any cluster point of the empirical averages…

In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…

This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…

This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…

Researchers are often interested in examining between-individual differences in within-individual processes. If the process under investigation is tracked for a long time, its trajectory may show a certain degree of nonlinearity, so that…

We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…

A well-known discovery of Feige's is the following: Let $X_1, \ldots, X_n$ be nonnegative independent random variables, with $\mathbb{E}[X_i] \leq 1 \;\forall i$, and let $X = \sum_{i=1}^n X_i$. Then for any $n$, \[\Pr[X < \mathbb{E}[X] +…

In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…

This article establishes a universal robust limit theorem under a sublinear expectation framework. Under moment and consistency conditions, we show that, for $\alpha \in(1,2)$, the i.i.d. sequence \[ \left \{ \left(…

Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…

The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in…

In this paper we extend the definition of time conditional G-expectations $\mathbb{\hat{E}}_{t}[\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time…

We derive two conditional expectation bounds, which we use to simplify cryptographic security proofs. The first bound relates the expectation of a bounded random variable and the average of its conditional expectations with respect to a set…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

A conditional expectation function (CEF) can at best be partially identified when the conditioning variable is interval censored. When the number of bins is small, existing methods often yield minimally informative bounds. We propose three…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$…