Related papers: Inequalities and bounds for expected order statist…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
It is well known that the traditional Jensen inequality is proved by lower bounding the given convex function, $f(x)$, by the tangential affine function that passes through the point $(E\{X\},f(E\{X\}))$, where $E\{X\}$ is the expectation…
In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…
Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order…
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear…
We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities…
The bounds for absolute moments of order statistics are established. Let $X_1,\dots ,X_n$ be independent identically distributed real-valued random variables and let $X_{1:n}\le \dots \le X_{n:n}$ be the corresponding order statistics. The…
This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…
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…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
The comparison of alternative rankings of a set of items is a general and prominent task in applied statistics. Predictor variables are ranked according to magnitude of association with an outcome, prediction models rank subjects according…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We…
In this paper, a link between monotonicity of deterministic dynamical systems and propagation of order by Markov processes is established. The order propagation has received considerable attention in the literature, however, this notion is…