Related papers: Stochastic domination for iterated convolutions an…
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 prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that…
Let $X$ be a random variable with distribution function $F,$ and $X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P\{X_{i:n}\leq x\}.$ Using majorization…
Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
First order stochastic dominance and monotone likelihood ratio are two partial orders on the $n$-probability simplex that play an important role in the establishment of structural results for MDPs and POMDPs. We study the strength of those…
In this paper we describe the alternative approach to the sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of a distribution of the argument maximum. For a centered…
We study the quantization errors for the doubling probability measures $\mu$ which are supported on a class of Moran sets $E\subset\mathbb{R}^q$. For each $n\geq 1$, let $\alpha_n$ be an arbitrary $n$-optimal set for $\mu$ of order $r$ and…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under…
In this paper, we construct a class of random measures $\mu^{\mathbf{n}}$ by infinite convolutions. Given infinitely many admissible pairs $\{(N_{k}, B_{k})\}_{k=1}^{\infty}$ and a positive integral sequence…
Stochastic dominance is a fundamental concept in decision-making under uncertainty and quantitative finance, yet its practical application is hindered by computational intractability due to infinitely many constraints. We introduce the…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we…
We study a class of stationary processes indexed by $\Z^d$ that are defined via minors of $d$-dimensional (multilevel) Toeplitz matrices. We obtain necessary and sufficient conditions for phase multiplicity (the existence of a phase…
Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum…
For probability vectors x and y, the catalytic majorization relation x prec_T y is defined to hold when there exists a probability vector z such that x otimes z is majorized by y otimes z. In this paper, an infinite family of functions is…
In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization…
We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators…