Related papers: Statistical Decision Theory Respecting Stochastic …
Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$…
The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data -> decision]. An SDF need not perform…
Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound…
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…
Stochastic dominance is a preference relation of uncertain prospect defined over a class of utility functions. While this utility class represents basic properties of risk aversion, it includes some extreme utility functions rarely…
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…
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…
We provide a novel characterization of the $n$-th degree bounded stochastic dominance (BSD) order, linking it to the risk tolerance of decision-makers and providing a decision-theoretic foundation for these stochastic orders. Our results…
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…
We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic…
This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to…
We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates…
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…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
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…
Motivated by recent work on monotone additive statistics and questions regarding optimal risk sharing for return-based risk measures, we investigate the existence, structure, and applications of Meyer risk measures. Those are monetary risk…
Safe Reinforcement Learning from Human Feedback (RLHF) typically enforces safety through expected cost constraints, but the expectation captures only a single statistic of the cost distribution and fails to account for distributional…
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
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…
The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk…