arXiv subjects

Xingwei Hu

Publications and source records attributed to Xingwei Hu.

9 recordsLinked to original sources

arXiv2025

Strong convergence rate of the positivity-preserving logarithmic truncated EM method for multi-dimensional stochastic differential equations with positive solutions

As a combination of the logarithmic transformation with the truncated Euler-Maruyama (TEM) scheme, the positivity-preserving logarithmic truncated Euler-Maruyama (LTEM) scheme has been generally developed for scalar stochastic differential equations (SDEs) with positive solutions. A subsequent question arises: can this method be extended to effectively solve general multidimensional SDEs with positive solutions? The answer to this question is affirmative. In this paper, we construct the positivity-preserving LTEM scheme to solve this type of system and demonstrate the suboptimal strong convergence rate of this scheme. On the other hand, when the underlying system degenerates into a scalar equation, the latest LTEM scheme analyzed by Tang & Mao (2024) is applicable to scalar SDEs with weak conditions, but its strong convergence rate is suboptimal. Based on this, we will theoretically demonstrate the optimal convergence rate of the LTEM method without infinitesimal factors in the scalar case. The proof strategy exactly improves its convergence rate from suboptimal to optimal. Finally, numerical examples are provided to validate the effectiveness and positivity-preserving of the LTEM method.

math.NA↗

arXiv2024

Strong convergence rate of positivity-preserving truncated Euler--Maruyama method for multi-dimensional stochastic differential equations with positive solutions

To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transformation. However, using these techniques often leads to the transformed stochastic differential equations (SDEs) not meeting the global monotonicity condition, particularly in multi-dimension case. This condition is essential for achieving strong convergence rates of numerical schemes. A pertinent question arises from this issue regarding the existence of an effective method with a convergence rate for solving multi-dimensional SDEs with positive solutions. This paper presents a positivity-preserving method that combines a novel truncated mapping with a truncated Euler--Maruyama discretization. We investigate both the strong convergence of the numerical method under some reasonable conditions. Furthermore, we demonstrate that this method achieves the optimal strong convergence order of 1/2 under certain additional assumptions. Numerical experiments are conducted to validate these theoretical results and demonstrate the positivity of the numerical solutions.

math.NA↗

arXiv2021

Decoding Causality by Fictitious VAR Modeling

In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the cause-effect relations within the data. Regression analysis, however, is generally for correlation relation, and very few researches have focused on variance analysis for causality discovery. We first set up an equilibrium for the cause-effect relations using a fictitious vector autoregressive model. In the equilibrium, long-run relations are identified from noise, and spurious ones are negligibly close to zero. The solution, called causality distribution, measures the relative strength causing the movement of all series or specific affected ones. If a group of exogenous data affects the others but not vice versa, then, in theory, the causality distribution for other variables is necessarily zero. The hypothesis test of zero causality is the rule to decide a variable is endogenous or not. Our new approach has high accuracy in identifying the true cause-effect relations among the data in the simulation studies. We also apply the approach to estimating the causal factors' contribution to climate change.

stat.ML↗

arXiv2021

Feature Selection by a Mechanism Design

In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.

stat.ML↗

arXiv2020

Globalization? Trade War? A Counterbalance Perspective

This paper investigates the evolving dynamics of international trade, emphasizing the strategic interplay between competition and cooperation within the global trade network. It argues that competitive advantages - rather than traditional comparative advantages - are the primary drivers of trade conflicts and deglobalization. Drawing on the concept of the balance of power, the paper introduces a quantitative measure of competitiveness, which complements the trade balance as a long-term policy objective. It further explores how countries can enhance competitiveness and trade balance through globalization, protectionism, collaboration, or trade frictions. Using real-world trade data from 2000 to 2019, our empirical study finds parallels between historical developments and quantitative evidence based on this new theory, offering actionable insights to policymakers for managing trade relations, mitigating conflicts, and calibrating the optimal level of globalization.

econ.GN↗

arXiv2020

Sorting Big Data by Revealed Preference with Application to College Ranking

When ranking big data observations such as colleges in the United States, diverse consumers reveal heterogeneous preferences. The objective of this paper is to sort out a linear ordering for these observations and to recommend strategies to improve their relative positions in the ranking. A properly sorted solution could help consumers make the right choices, and governments make wise policy decisions. Previous researchers have applied exogenous weighting or multivariate regression approaches to sort big data objects, ignoring their variety and variability. By recognizing the diversity and heterogeneity among both the observations and the consumers, we instead apply endogenous weighting to these contradictory revealed preferences. The outcome is a consistent steady-state solution to the counterbalance equilibrium within these contradictions. The solution takes into consideration the spillover effects of multiple-step interactions among the observations. When information from data is efficiently revealed in preferences, the revealed preferences greatly reduce the volume of the required data in the sorting process. The employed approach can be applied in many other areas, such as sports team ranking, academic journal ranking, voting, and real effective exchange rates.

stat.ML↗

arXiv2020

A Theory of Dichotomous Valuation with Applications to Variable Selection

An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables, we derive a valuation framework by the expected marginal gain and marginal loss in all potential modeling scenarios. However, marginal gain and loss are not symmetric; thus, we introduce three unbiased solutions. When used in variable selection, our new approaches significantly outperform several popular methods used in practice. The results also explore some novel traits of the Shapley value.

stat.ML↗

arXiv2018

Analytical Standard Errors for Exploratory Factor Solutions

Inference for factor models is often hampered by the lack of tractable and accurate variance estimates, which can materially distort downstream analyses. In practice, uncertainty in the residual covariance matrix is frequently either ignored or addressed through computationally intensive resampling methods that tend to be unstable. This paper develops a unified analytical framework for inference in exploratory factor analysis under several widely used extraction rules, including least-squares, principal-factor, iterative principal-component, alpha, and image factoring. By treating these estimators as implicitly defined functions of the sample covariance matrix, we derive closed-form Jacobians that translate perturbations in the covariance matrix into changes in the resulting factor solutions. Combined with the delta method and consistent estimators of the sample covariance matrix, the proposed approach yields standard errors that are straightforward to compute and remain valid under non-Gaussianity, heteroskedasticity, and serial or cross-sectional dependence. Simulation evidence confirms that the analytical standard errors accurately capture finite-sample variability while avoiding both the instability of bootstrap procedures and the restrictive assumptions underlying Fisher information-based inference. An application to a factor-augmented structural vector autoregressive (SVAR) model further demonstrates how accounting for this source of uncertainty can substantially affect impulse-response inference. Taken together, the results provide a practical and general tool for propagating estimation uncertainty in settings where factor extraction serves as an intermediate step.

math.ST↗

arXiv2018

A Dichotomous Analysis of Unemployment Benefits

This paper introduces a novel framework for designing fair and sustainable unemployment benefits, grounded in cooperative game theory and real-time fiscal policy. The labor market is modeled as a coalitional game, where a random subset of participants is employed, generating stochastic economic output. To ensure fairness, we adopt equal employment opportunity as a normative benchmark and propose a dichotomous valuation rule that assigns value to both employed and unemployed participants. Within a continuous-time, balanced budget framework, we derive a closed-form payroll tax rate that is fair, debt-free, and asymptotically risk-free. This tax rule is robust across alternative objectives and promotes employment, productivity, and equality of outcome. The framework naturally extends to other domains involving random bipartitions and shared payoffs, such as voting rights, health insurance, road tolling, and feature selection in machine learning. Our approach offers a transparent, theoretically grounded policy tool for reducing poverty and economic inequality while maintaining fiscal discipline.

q-fin.GN↗