This paper introduces a robust specification test for linear regression built on a rank-score empirical process. The proposed test is distribution-free, easy to implement, and accommodates a broad class of score functions. We derive the asymptotic properties of the test statistics under the null, fixed alternatives, and a sequence of local alternatives. To implement the test in finite samples, we employ a simple multiplier bootstrap procedure with establishing its asymptotic validity. Simulations and an empirical application indicate reliable size and strong power with notable robustness to heavy-tailed errors and outliers.

MOTIVATION:Hi-C is a powerful technology for mapping chromatin interactions genome-wide. However, interaction loops identified from Hi-C contact maps often vary across replicate experiments due to experimental noise, making reproducibility assessment essential. A major challenge lies in the genomic distance dependence of interaction strength, which systematically affects reproducibility but is overlooked by existing methods for reproducibility assessment. RESULTS:We introduce Stratum-Adjusted Irreproducible Discovery Rate (SIDR), a novel statistical model that integrates distance stratification into the widely-used Irreproducible Discovery Rate (IDR) framework. SIDR explicitly models the confounding effect of genomic distance, enabling global control of irreproducibility across interaction ranges. Through simulations and real Hi-C datasets, we demonstrate that SIDR improves discriminative power and recovers more biologically meaningful interactions than existing approaches, making it a valuable tool for robust and reproducible Hi-C analysis. AVAILABILITY:The R package SIDR is freely available on GitHub https://github.com/qunhualilab/SIDR.

The rapid development of green finance has reshaped the structure of China's financial system. Understanding how green finance interacts with traditional financial markets is essential for maintaining market stability and supporting low-carbon transition. This study examines the time-varying causal relationship between green finance and traditional financial markets in China across multiple frequency scales. Methodologically, we apply Ensemble Empirical Mode Decomposition (EEMD) and a time-varying Granger causality framework to capture dynamic and scale-dependent effects. Empirical results show that the overall causal connections are relatively weak. However, bond prices exert a significant influence on both carbon and green bond markets. The carbon market mainly affects stock prices during periods of policy adjustment, while bond market movements consistently shape green bond dynamics. Multi-scale analysis further shows that short-term causal effects are temporary and largely driven by event shocks. In contrast, medium- and long-term causal effects between green finance and traditional financial markets are more persistent and stable. These findings suggest that strengthening coordination between green finance and traditional financial markets is crucial for enhancing financial stability and promoting sustainable development in China.

As digital finance expands rapidly in emerging economies, understanding its nonlinear impact on green economic efficiency is critical for sustainable development. This article investigates this relationship in China by employing a regression kink model with an unknown threshold. We identify a structural breakpoint that previous approaches failed to capture. The kink specification imposes continuity while allowing asymmetric slope changes - better reflecting the gradual evolution of digital infrastructure and institutions. We find a V-shaped pattern: below a threshold (DF index approximate to 52.90), digital finance suppresses green efficiency; above it, the effect turns positive. These findings provide actionable guidance for China's Dual Carbon goals and offer a benchmark for other emerging economies pursuing green transformations.

This study develops a multi-layer local Gaussian correlation network approach to examine crisis-specific commodity - inflation linkages across the G7 and E7 economies. The empirical results show that mean inflation correlations between the E7 and G7 are lower than within-group correlations, suggesting differences in inflation co-movements between advanced and emerging economies. Energy - inflation linkages are generally stronger than both cross-country inflation linkages and agricultural commodity - inflation associations, with all correlations rising noticeably during major global crises. These patterns also display clear quantile heterogeneity. At the low inflation quantile, commodity - inflation linkages are relatively broad-based across the G7 and E7 economies, whereas they become denser and more concentrated at higher inflation quantiles. Major crises also reshape the network structure in distinct ways. The 2008 crisis is marked by the central role of agricultural commodities, the COVID-19 pandemic by a more balanced energy - agriculture pattern, and the 2022 Russia - Ukraine war by the prominence of the Russia - natural gas linkage. Overall, the results suggest that commodity - inflation linkages are shaped jointly by inflation regimes, commodity characteristics, and crisis-specific structural shocks. The findings also provide useful implications for policymakers in designing tailored response strategies that take account of quantile-dependent risks and event-driven vulnerabilities in global commodity markets.

As climate change intensifies and the Paris Agreement is enacted, climate risk has become one of the major challenges for global economy and financial system. This study proposes an expectile-on-expectile regression (EER) model to analyze asymmetric and nonlinear impacts of Physical Risk Index (PRI) and Transition Risk Index (TRI) respectively on carbon return from January 2, 2009, to June 28, 2024, comparing pre- and post-Paris Agreement periods. The results show the impacts of PRI and TRI on carbon return are not the same, and for each climate risk, the impact patterns are also different pre- and post-Paris Agreement. Specifically, Pre-Paris, PRI exposured reduced carbon return at low expectiles (especially in adverse markets) but was positive at high returns. Post-Paris, PRI effects reversed: strongly positive at low returns and negative at high returns. This indicates the Paris Agreement institutionalized climate risk considerations, turning carbon markets from passive risk mitigation to active risk pricing and inverting the climate risk-carbon return relationship. TRI’s impact also varies across expectiles, with positive effects at low carbon return (more pronounced pre-Paris) that diminish or turn negative at higher expectiles, which is more volatile pre-Agreement. These shifts suggest that the Paris Agreement’s enhanced climate disclosures and regulatory scrutiny have fostered more systematic risk pricing, reducing excessive market fluctuations. Overall, the findings highlight the Agreement’s pivotal role in realigning carbon market behavior with climate-related financial risks, driven by growing climate awareness and institutional reforms.

In this paper, we propose a novel weighted modal regression neural network (WMRNN) for analyzing right-censored data. WMRNN provides a flexible nonlinear framework for modeling the conditional mode of the response variable based on covariates. This method excels in predicting the most likely outcomes and enhances predictive accuracy, effectively managing survival data even when it exhibits asymmetric, peaked, or heavy-tailed distributions. It functions well regardless of the independence of censoring variable from covariates. By harnessing the nonlinear capabilities of deep neural networks within the modal regression framework, WMRNN addresses random censoring using inverse probability of censoring weighting (IPCW) in its loss function. This approach eliminates the need for predetermined functional forms, allowing for greater adaptability. Extensive simulations and two real-world case studies demonstrate the strong performance of WMRNN in predicting outcomes from right-censored data, highlighting its potential as a valuable tool in survival analysis.

As an alternative to quantile regression, expectile regression can also draw the complete picture of the response and characterise the heterogeneity of the data. However, there is limited study on testing for Granger-causality in expectiles. This paper aims to develop a sup-Wald test for Granger non-causality in an expectile range. The asymptotic null distribution and local power properties of the test are derived for stationary time series. A simulated test procedure is proposed to approximate the critical values by simulating the Gaussian process that characterises the limiting distributions of the test statistic. Simulation studies demonstrate that our test has reasonable size and good power under different model settings. Our test is applied to detect volatility spillover effects between the crude oil and stock markets in the US, Germany and France during the COVID-19 pandemic. The empirical results indicate higher volatility spillovers and significant asymmetric spillover effects between oil and stock markets, with market-specific heterogeneity.

This article introduces a threshold expectile regression model with an unknown threshold for dependent data, which enables simple characterization of nonlinearity and heteroscedasticity in economic and financial applications. Profile estimation is proposed for the unknown parameters, and a sup-Wald test is developed to test the existence of the threshold effect at a fixed expectile level. Inference issues across multiple expectile levels are further considered, with a likelihood-ratio-type test designed to check for the presence of a common threshold value. Monte Carlo simulations demonstrate the nice finite sample performance of the proposed inference procedures. Finally, an empirical application demonstrates that the debt-to-GDP ratio has a heterogeneous threshold effect on the U.S. growth rate across the growth distribution.

Expectile is a coherent and elicitable law-invariant risk measure widely applied in risk management. Existing methods based on iteratively reweighted least squares (IWLS) are not computationally efficient for large-scale sample sizes. To overcome the issue, we develop a direct nonparametric conditional expectile function estimator by inverting the local polynomial estimator of the conditional loss-gain function. The proposed estimator is computationally friendly and stable without using iterative algorithms that require computation with large-scale data in each iteration. We establish the asymptotic distribution of the proposed estimator. We further show that the proposed estimator has a smaller variance than the existing IWLS estimator and a smaller mean square error in various scenarios. Simulations confirm the computational and statistical efficiency of the proposed method. We further apply the proposed methods to an S&P500 data set to illustrate the computational time to estimate the conditional expectile-based value-at-risk (EVaR) and the precision in out-of-sample prediction.

The expectile-based value-at-risk (EVaR) has been attracted attention recently in financial risk management, because it is the only coherent and elicitable risk measure. However, since there is no closed-form solution for minimizing the expectile-loss function, the existing nonparametric estimator for EVaR usually requires an additional iterative algorithm. This paper presents a new alternative nonparametric estimator for EVaR for dependent financial returns. The proposed estimator is computationally easy to implement by existing software, without any extra iterative computation burdens. We also establish its asymptotic properties for statistical inference, including the strong consistency and asymptotic normality. Monte Carlo simulations demonstrate its good performance being comparable to the existing estimator in terms of bias and mean squared error, but outperforming the existing estimator in terms of computational efficiency. Two empirical applications of the US dollar index data and S&P500 index data are conducted to illustrate the method. The results show that our proposed estimator is better than compared estimator in EVaRs forecasting with smaller associated realized losses and less computation time.

It is a key issue for determining the optimal treatment regime or a sequence of treatment regimes based on individual characteristics in precision medical research. Most existing studies on estimating optimal treatment regimes focus on maximizing the average return on the potential outcomes of interest. However, this approach fails to capture the potential heterogeneity of observations and can not provide a complete characterization of the data. Expectiles, derived from an asymmetric quadratic loss function, encompass the mean and serve as a valuable tool for describing the distribution of outcomes. Motivated by these advantages of expectiles, we propose novel estimators for both static and dynamic expectile-optimal treatment regimes. Due to the differentiability of the loss function, it can bring computational advantages and facilitates theoretical analysis. The asymptotic properties of the proposed estimators are derived using empirical process theory. Their good finite sample performances are demonstrated through simulations and a real data from the HIV patients.

The Regional Comprehensive Economic Partnership (RCEP) has brought both opportunities and new challenges to the Asia-Pacific financial markets. To analyze the spillover effects of stock market risk among RCEP countries, this paper constructs a comprehensive framework for systemic risk management encompassing three aspects: risk measurement, connectivity analysis and identification of influential factors. Specifically, we apply the CoES as a risk measurement metric to construct a tail risk network. Based on risk decomposition in sliding windows, we examine the hierarchical propagation pathways, intensities and evolution mechanisms of systemic risk in RCEP stock markets across four levels (system, group, country and institution). Subsequently, we use a tail-event driven dynamic network quantile regression (TEDNQR) model to explore the influence of network topology, node heterogeneity, and common factors on stock price changes across different quantile levels. Finally, we employ robustness analysis based on goodness-of-fit and DM test to validate the reliability of our methodology and conclusions. The empirical results indicate that both the risk performance and the influential factors of RCEP stock markets exhibit time-varying and tail characteristics. Overall, simultaneous network effects significantly and positively impact stock movements, playing a dominant role among all factors.

Large language models (LLMs) have shown impressive performance on downstream tasks through in-context learning (ICL), which heavily relies on the demonstrations selected from annotated datasets. Existing selection methods may hinge on the distribution of annotated datasets, which can often be long-tailed in real-world scenarios. In this work, we show that imbalanced class distributions in annotated datasets significantly degrade the performance of ICL across various tasks and selection methods. Moreover, traditional rebalance methods fail to ameliorate the issue of class imbalance in ICL. Our method is motivated by decomposing the distributional differences between annotated and test datasets into two-component weights: class-wise weights and conditional bias. The key idea behind our method is to estimate the conditional bias by minimizing the empirical error on a balanced validation dataset and to employ the two-component weights to modify the original scoring functions during selection. Our approach can prevent selecting too many demonstrations from a single class while preserving the effectiveness of the original selection methods. Extensive experiments demonstrate the effectiveness of our method, improving the average accuracy by up to 5.46 on common benchmarks with imbalanced datasets.

This article proposes a novel quantile regression model, called the linear-quadratic quantile regression model, which can capture the nonlinear effect of a covariate on the response variable. It is actually a two-segmented quantile regression model, in the sense that the linear term associated with a continuous exposure in standard quantile regression is replaced by a linear term and a quadratic term below and above an unknown change point, respectively. A two-step estimation procedure is proposed to estimate the regression coefficients and the change point at a given quantile level. The asymptotic properties of the proposed estimator are derived by the empirical process theory, and the change point estimator is shown to achieve standard root-n consistency. A sup-Wald test is developed to test the existence of a change-point at a given quantile level. Furthermore, estimation and inference procedures for linear-quadratic quantile regression across multiple quantile indices are presented. Particularly, the test and inference for the common threshold across different quantile indices are proposed. Monte Carlo simulations and an empirical application to GDP per capita illustrate the practical usefulness of the proposed method.

This paper provides a comprehensive reassessment of gold's role as a safe haven, hedge, and portfolio diversifier across the stock markets of G7 and E7 countries from January 1, 2000, to December 31, 2024. We employ an integrated empirical framework, combining quantile-onquantile (QQ) regression, causality-in-quantiles testing, and the cross-quantilogram method. This approach allows us to capture asymmetric and heterogeneous dependencies across the joint distribution of gold and stock returns. The findings reveal that gold acts as a safe haven during market downturns in most G7 countries, particularly where gold comprises a large share of official reserves. In contrast, gold typically serves as a diversifier in E7 countries. However, under specific asymmetric market conditions, gold exhibits hedging or safe-haven behavior in some E7 countries, such as Turkey, India, and Brazil. The results also highlight the role of gold reserve composition in enhancing gold's safe-haven properties. In countries with substantial official gold holdings, gold demonstrates more robust safe-haven capabilities. The causality-in-quantiles analysis further confirms bidirectional and nonlinear predictive relationships across quantiles, while recursive and sub-sample QQ estimations indicate that the safe-haven function of gold is time-varying and evolves in response to systemic shocks. These findings provide valuable insights for both investors and policymakers by highlighting the varying effectiveness of gold as a risk management instrument across various markets and economic conditions, emphasizing the importance of tailored strategies in uncertain financial environments.

Identifying the primary factors driving the interconnectedness between stock and bond markets is critical for portfolio decision-making and risk management. This study proposes an adaptive Lasso-DCC-MIDAS model with multiple explanatory variables. It enables us to investigate the long-term and short-term correlation between different markets, examine the impact of various macroeconomic and financial factors on market comovement and identify the primary drivers. Our empirical findings indicate that during economic booms, the comovement between China's stock and bond markets is strengthened and positive, exhibiting ‘synchronization’. Conversely, during recessions, it is often weakened and negative, showing ‘asynchrony’. Further analysis reveals that the turnover rates and the real effective exchange rate of the stock market are the dominant driving force and these impact changes dynamically with the state of the market. Our empirical findings can not only help us gain a better understanding of the underlying drivers of market dynamics and make more informed investment decisions but also be useful for policymakers in developing macroeconomic policies that promote stability and growth in financial markets.

As China advances toward achieving its dual carbon goals, corporate ESG levels are increasingly gaining attention from investors. To provide investors with more empirical references for ESG-level investing, this paper incorporates corporate ESG levels as a new factor into the traditional Fama-French six-factor model. It examines the risk premium effect of the ESG factor while correcting the omission bias of the traditional six-factor model regarding market anomalies. Empirical results reveal a significant negative ESG factor premium effect in China's A-share market, contrasting with the U.S. market. This study deepens investor understanding of ESG levels and provides empirical evidence for relevant policy formulation.