Ruodu Wang
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View article: Elicitability and Identifiability of Tail Risk Measures
Elicitability and Identifiability of Tail Risk Measures Open
Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value‐at‐Risk, Expected Shortfall (ES) and Range Value‐at‐Risk being prime examples. They are induced by law‐ba…
View article: Invariant Modeling for Joint Distributions
Invariant Modeling for Joint Distributions Open
A common theme underlying many problems in statistics and economics involves the determination of a systematic method of selecting a joint distribution consistent with a specified list of categorical marginals, some of which have an ordina…
View article: Choquet rank-dependent utility with an exogenous unambiguous source
Choquet rank-dependent utility with an exogenous unambiguous source Open
We axiomatize the Choquet rank-dependent utility model within a Savage framework with an exogenous source of pure risk. This model is a decision model under ambiguity, serving as a conceptual generalization of the Choquet expected utility …
View article: Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence
Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence Open
Heavy-tailed combination tests, such as the Cauchy combination test and harmonic mean p-value method, are widely used for testing global null hypotheses by aggregating dependent p-values. However, their theoretical guarantees under general…
View article: Subuniformity of harmonic mean p$$ p $$‐values
Subuniformity of harmonic mean p$$ p $$‐values Open
We obtain several inequalities on the generalized means of dependent ‐values. In particular, the weighted harmonic mean of ‐values is strictly subuniform under several dependence assumptions of ‐values, including independence, negative upp…
View article: A duality between utility transforms and probability distortions
A duality between utility transforms and probability distortions Open
In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility, …
View article: Eliciting reference measures of law-invariant functionals
Eliciting reference measures of law-invariant functionals Open
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
View article: Choquet rating criteria, risk measures, and risk consistency
Choquet rating criteria, risk measures, and risk consistency Open
Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely rela…
View article: Combining exchangeable <i>P</i> -values
Combining exchangeable <i>P</i> -values Open
The problem of combining P -values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily depe…
View article: On convex order and supermodular order without finite mean
On convex order and supermodular order without finite mean Open
Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…
View article: Quadratic-form Optimal Transport
Quadratic-form Optimal Transport Open
We introduce the framework of quadratic-form optimal transport (QOT), whose transport cost has the form $\iint c\,\mathrm{d}π\otimes\mathrm{d}π$ for some coupling $π$ between two marginals. Interesting examples of quadratic-form transport …
View article: The only admissible way of merging arbitrary <i>e</i>-values
The only admissible way of merging arbitrary <i>e</i>-values Open
In this paper it is proved that the only admissible way of merging arbitrary $ e $-values is to use a weighted arithmetic average. This result completes the picture of merging methods for arbitrary $ e $-values and generalizes the result o…
View article: Quantiles under ambiguity and risk sharing
Quantiles under ambiguity and risk sharing Open
Choquet capacities and integrals are central concepts in decision making under ambiguity or model uncertainty, pioneered by Schmeidler. Motivated by risk optimization problems for quantiles under ambiguity, we study the subclass of Choquet…
View article: Prudence and higher-order risk attitudes in the rank-dependent utility model
Prudence and higher-order risk attitudes in the rank-dependent utility model Open
We obtain a full characterization of consistency with respect to higher-order stochastic dominance within the rank-dependent utility model. Different from the results in the literature, we do not assume any condition on the utility functio…
View article: Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures
Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures Open
We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convoluti…
View article: Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values
Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values Open
This half-size MFO workshop brings together researchers in mathematical statistics, probability theory, machine learning, medical sciences, and economics to discuss recent developments in sequential inference. New sequential inference meth…
View article: The reference interval in higher-order stochastic dominance
The reference interval in higher-order stochastic dominance Open
Given two random variables taking values in a bounded interval, we study whether one dominates the other in higher-order stochastic dominance depends on the reference interval in the model setting. We obtain two results. First, the stochas…
View article: Diversification quotient based on expectiles
Diversification quotient based on expectiles Open
A diversification quotient (DQ) quantifies diversification in stochastic portfolio models based on a family of risk measures. We study DQ based on expectiles, offering a useful alternative to conventional risk measures such as Value-at-Ris…
View article: Hypothesis testing with e-values
Hypothesis testing with e-values Open
This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce…
View article: True and false discoveries with independent and sequential <i>e</i>‐values
True and false discoveries with independent and sequential <i>e</i>‐values Open
In this article, we use e ‐values in the context of multiple hypothesis testing, assuming that the base tests produce independent, or sequential, e ‐values. Our simulation and empirical studies, as well as theoretical considerations, sugge…
View article: Testing the mean and variance by <i>e</i>-processes
Testing the mean and variance by <i>e</i>-processes Open
Summary We address the problem of testing the conditional mean and conditional variance for nonstationary data. We build e-values and p-values for four types of nonparametric composite hypothesis with specified mean and variance as well as…
View article: Asymptotic and compound e-values: multiple testing and empirical Bayes
Asymptotic and compound e-values: multiple testing and empirical Bayes Open
We explicitly define the notions of (bona fide, approximate or asymptotic) compound p-values and e-values, which have been implicitly presented and used in the recent multiple testing literature. While it is known that the e-BH procedure w…
View article: Improved thresholds for e-values
Improved thresholds for e-values Open
The rejection threshold used for e-values and e-processes is by default set to $1/α$ for a guaranteed type-I error control at $α$, based on Markov's and Ville's inequalities. This threshold can be wasteful in practical applications. We dis…
View article: Infinite-mean models in risk management: Discussions and recent advances
Infinite-mean models in risk management: Discussions and recent advances Open
In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be …