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Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
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…
Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has…
Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of interference distributions in large-scale…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
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…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
We construct a procedure to test the stochastic order of two samples of interval-valued data. We propose a test statistic which belongs to U-statistic and derive its asymptotic distribution under the null hypothesis. We compare the…
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…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…