arXiv subjects

Arie Beresteanu

Publications and source records attributed to Arie Beresteanu.

6 recordsLinked to original sources

arXiv2026

Partial Identification with Auxiliary Moment Restrictions

Partial identification is often set aside in practice because the identification regions it delivers are too wide to be useful, pushing researchers toward strong assumptions that buy point identification at the cost of credibility. We show that a source of information already sitting in most interval-valued datasets can fix this without adding any assumption at all. When an outcome is reported only as an interval---because a data custodian bracketed, top-coded, or formally privatized it to protect respondents---the same custodian typically continues to publish accurate population aggregates of that outcome, precisely because doing so does not compromise any individual record. We develop a framework for exploiting exactly this information: restricting the set of admissible completions of the data to those consistent with a known aggregate, rather than restricting the interval itself, and characterizing the sharp identification region that results for the best linear predictor. The restrictions we study behave in strikingly different ways---some collapse the region by a full dimension, others narrow it while leaving its shape intact. We characterize the geometric effect of each restriction and derive closed-form directional measures of identifying value for the mean and conditional-mean cases. An illustration using interval-valued wages from the Current Population Survey shows that the effect is far from marginal: modest auxiliary information recovers a substantial share of the identifying power usually thought to be lost once an outcome is coarsened.

econ.EM↗

arXiv2026

Bounds for Restricted Selections of Random Sets

We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the restricted selection set and establish sharp bounds on the attainable ranges of means, medians, and event probabilities. In particular, we give conditions under which every value in the Aumann expectation range is realized as the mean of a measurable selection, and we obtain explicit formulas for the extremal expectations under median and higher-moment restrictions via rearrangement and convex-duality arguments. We further show that the selection set of any random compact convex set in $\R^d$ can be approximated in $L^1$ by selection sets of disjoint unions of random cubes, each of which decomposes coordinate-wise into one-dimensional interval selection problems. This gives us an approximation-based reduction of constrained selection problems for random compact convex sets in $\R^d$.

math.PR↗

arXiv2025

Beyond Scalars: Zonotope-Valued Utility for Representation of Multidimensional Incomplete Preferences(Incomplete Version)

In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional approaches assign single numerical values to alternatives, failing to capture the complexity of preferences where alternatives remainmain incomparable due to conflicting criteria across multiple dimensions. Our method maps each alternative to a zonotope, a convex geometric object in $\mathbb{R}^m$ formed by Minkowski sums of intervals, which encapsulates the multidimensional structure of preferences with mathematical rigor. The set-valued nature of these payoffs stems from multiple sources, including non-probabilistic uncertainty, such as imprecise utility evaluation due to incomplete information about criteria weights, and probabilistic uncertainty arising from stochastic decision environments. By decomposing preference relations into interval orders and utilizing an extended set difference operator, we establish a rigorous axiomatization that defines preference as one alternative's zonotope differing from another's within the non-negative orthant of $\mathbb{R}^m$. This framework generalizes existing representations and provides a visually intuitive and theoretically robust tool for modeling trade-offs among each dimension, while preferences are incomparable.

econ.TH↗

arXiv2025

Extended Set Difference : Inverse Operation of Minkowski Summation

This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such sets, offering a broader framework for set arithmetic. The difference may not be necessarily unique, but we offer a bound on the variety of solutions. The definition of the extended set difference is formulated through an optimization problem, which provides a constructive approach to its computation. The paper explores the properties of this new difference, including its stability under orthogonal transformations and its robustness to perturbations of the input sets. We propose a method to compute this difference through a formulated linear optimization problem.

math.OC↗

arXiv2025

Identification of Incomplete Preferences

We provide a sharp identification region for discrete choice models where consumers' preferences are not necessarily complete even if only aggregate choice data is available. Behavior is modeled using an upper and a lower utility for each alternative so that non-comparability can arise. The identification region places intuitive bounds on the probability distribution of upper and lower utilities. We show that the existence of an instrumental variable can be used to reject the hypothesis that the preferences of all consumers are complete. We apply our methods to data from the 2018 mid-term elections in Ohio.

econ.EM↗

arXiv2020

Quantile Regression with Interval Data

This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for regular random variables. We then give sharp characterization of this set by extending concepts from random set theory. For quantile regression parameters, we show that the identification set is characterized by a system of conditional moment inequalities. This characterization extends that of parametric quantile regression for regular random variables. Estimation and inference theories are developed for continuous cases, discrete cases, nonparametric conditional quantiles, and parametric quantile regressions. A fast computational algorithm of set linear programming is proposed. Monte Carlo experiments support our theoretical properties.

stat.ME↗