Related papers: Moment bounds for IID sequences under sublinear ex…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
In this note, we will survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity…
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…
This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these…
Information-theoretic generalization bounds based on the supersample construction are a central tool for algorithm-dependent generalization analysis in the batch i.i.d.~setting. However, existing supersample conditional mutual information…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…
For probabilistic programs, it is usually not possible to automatically derive exact information about their properties, such as the distribution of states at a given program point. Instead, one can attempt to derive approximations, such as…
We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under…
The paper concerns the optimal upper bounds on the expectations of the kth record values (k >= 1) centered about the sample mean. We consider the case, when the records are based on the infinite sequence of the independent identically…
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the extent to which this inequality can be violated has been a…
Let $X_1,\ldots,X_n$ be independent identically distributed random vectors in $\mathbb{R}^d$. We consider upper bounds on $\max_x \mathbb{P}(a_1X_1+\cdots+a_nX_n=x)$ under various restrictions on $X_i$ and the weights $a_i$. When…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We study the nonlinear fractional stochastic heat equation in the spatial domain $\mathbb{R}$ driven by space-time white noise. The initial condition is taken to be a measure on $\mathbb{R}$, such as the Dirac delta function, but this…
In this paper we study the distribution tails and the moments of a condition number which arises in the study of homogeneous systems of linear inequalities. We consider the case where this system is defined by a Gaussian random matrix and…
In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independent, symmetric and satisfy the moment growth condition…
In this paper, we solve the existence problem of optimal stopping problem under some kind of nonlinear expectation named g_\Gamma expectation which was recently introduced in Peng, S.G. and Xu, M.Y. [8]. Our method based on our preceding…
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…