Related papers: Multidimensional Stochastic Dominance Test Based o…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
This paper introduces a novel test for conditional stochastic dominance (CSD) at specific values of the conditioning covariates, referred to as target points. The test is relevant for analyzing income inequality, evaluating treatment…
Stochastic multi-objective optimization (SMOOP) requires ranking multivariate distributions; yet, most empirical studies perform scalarization, which loses information and is unreliable. Based on the optimal transport theory, we introduce…
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…
We introduce a 2-dimensional stochastic dominance (2DSD) index to characterize both strict and almost stochastic dominance. Based on this index, we derive an estimator for the minimum violation ratio (MVR), also known as the critical…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
The statistical decision theory pioneered by Wald (1950) has used state-dependent mean loss (risk) to measure the performance of statistical decision functions across potential samples. We think it evident that evaluation of performance…
Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However,…
Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…
In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random…
Introduced by M\"uller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed…
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Based on measure transportation ideas, several attempts have…
Univariate concepts as quantile and distribution functions involving ranks and signs, do not canonically extend to $\mathbb{R}^d, d\geq 2$. Palliating that has generated an abundant literature. Chapter 1 shows that, unlike the many…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
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,…
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
We consider a problem of finding an SSD (second-order stochastic dominance)-minimal quantile function subject to the mixture of FSD (first-order stochastic dominance) and SSD constraints. The SSD-minimal solution is explicitly worked out…
The use of Kolmogorov-Smirnov-type statistics for testing stochastic dominance goes back to McFadden (1989). In this paper we extend the approach of Barret and Donald (2003) to the bivariate case, without the assumption of absolute…