Related papers: Convergences of Random Variables under Sublinear E…
Linear combinations of independent random variables have been extensively studied in the literature. However, most of the work is based on some specific distribution assumptions. In this paper, a companion of (J. Appl. Probab. 48 (2011)…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
M-dependence is a commonly used assumption in the study of dependent sequences. In this paper, central limit theorems for m-dependent random variables under the sub-linear expectations are established based mainly on the conditions of…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
In this paper, we prove the equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent, identically distributed random variables under sublinear expectations space. As applications, the…
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
It is known that limit theorems for triangular arrays with identically distributed rows yields convergence of densities rather than just convergence in distribution. We show that this superconvergence result holds -- at least at points at…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
The present paper is devoted to the second part of our project on asymmetric maximal inequalities, where we consider martingales in continuous time. Let $(\mathcal M,\tau)$ be a noncommutative probability space equipped with a continuous…
This paper studies predictor functions motivated by maximizing a measure of agreement with the predictand. Specifically, it examines distributional properties and predictive performance of the estimated maximum agreement linear predictor…
We give an elementary proof of the fact that a binomial random variable $X$ with parameters $n$ and $0.29/n \le p < 1$ with probability at least $1/4$ strictly exceeds its expectation. We also show that for $1/n \le p < 1 - 1/n$, $X$…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
In this paper, we examine the fundamental performance limits of prediction, with or without side information. More specifically, we derive generic lower bounds on the $\mathcal{L}_p$ norms of the prediction errors that are valid for any…
We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Let $\{X_n;n\ge 1\}$ be a sequence of independent and identically distributed random variables in a regular sub-linear expectation space $(\Omega,\mathscr{H},\widehat{\mathbb E})$ with the finite Choquet expectation, upper mean…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.