28 March 2026, Volume 46 Issue 4

    

• Select all
  |

• Select
  Honour One and You Honour Them All——ESG Rating and Multi-Dimensional Risk of Listed Companies

  KANG Jijia, YANG Xiaoguang

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1039-1063. https://doi.org/10.12341/jssms241052

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Using ESG rating data of Sino-Securities Index Information Service from 2009 to 2020, this paper examines the impact of listed companies' ESG rating on the level of stock price, financial and operational risk in the next year. The study finds that better ESG rating has a significant inhibitory effect on all three risk levels of enterprises in the next year. Specifically, for the risk of stock price crash, ESG rating higher than the benchmark level, as a strong market signal, has a more significant reduction in the risk level of stock price crash. The trading volume of individual stocks, which reflects the attention of investors, has an intermediary effect on ESG to reduce the risk of enterprise stock price crash. ESG of large-scale enterprises that occupy an important position in the market and attract more attention from investors has a stronger inhibitory effect on the risk of stock price crash; In addition, the negative relationship between ESG and the risk of stock price crash is more significant after the implementation of the “Environmental Protection Law”. For financial risk, ESG has a marginal diminishing effect on reducing corporate financial risk, and the improvement of ESG rating from low to medium can improve the level of corporate financial risk. At the same time, enterprises' voluntary disclosure of non-financial information could strengthen the inhibitory effect of ESG on financial risks. For operational risk, ESG rating has a marginal diminishing effect on reducing operational risk; At the same time, the nature of equity has a moderating effect on the reduction of operating risks by ESG rating. Compared with private enterprises, ESG has a stronger inhibition effect on the operation risk of state-owned enterprises. Finally, the sub-sample heterogeneity test results based on the length of enterprise life in this paper show that the inhibitory effect of ESG rating on risk is stronger for enterprises with a long establishment age, but weaker for enterprises with a short establishment age.
• Select
  The Mediating Role of Stock Forums in the Stock Market: Investor Attention or Sentiment?

  LI Yue, ZHANG Yongjie, SHEN Dehua

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1064-1085. https://doi.org/10.12341/jssms240621

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Based on investor behavior data from the Eastmoney Guba, this paper employs the effective transfer entropy method to investigate whether the mediating role of stock forums in the stock market better represents investor attention or sentiment. The findings reveal that: 1) Investor attention in stock forums conveys more valuable information flows to the stock market, providing a more accurate representation of investor behavior; 2) The net comment volume, as a key indicator of investor attention, exhibits strong information flow correlations with the stock market, significantly influencing stock volatility, with its effect extending up to one month into the future; 3) Across posts with different sentiments (positive, neutral, and negative), investor attention consistently transmits information flows that predict stock volatility, while investor sentiment lacks significant incremental value in transmitting information flows to the market. This study further underscores the mediating role of stock forums in capturing investor attention, particularly highlighting the unique predictive value of net comment volume, offering investors a novel perspective on analyzing online stock forum data. Future research should focus on integrating more comprehensive datasets and conducting in-depth explorations to enhance the accuracy of market forecasts and the scientific rigor of investment decision-making.
• Select
  Research on the Evolutionary Game Model of Smart Elderly Care Services with the Participation of Four Parties

  SUN Shiwei, LI Xiahe, LI Yaoyao, LI Peilun, YAN Zhijun

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1086-1105. https://doi.org/10.12341/jssms240673

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  This study aims to delineate an integrated evolutionary game model for the smart elderly care service system by constructing an integrated evolutionary game model. The model encompasses four key stakeholders: Government agencies, smart elderly care service providers, digital platform operators, and the elderly user group. Employing the game model approach that scrutinizes the interactive dynamics and strategic choices among these stakeholders, we unveil the collaborative mechanisms within the smart elderly care service sector. The research findings suggest that strengthening cooperation among the government, enterprises, digital platforms, and the elderly population can effectively promote the development of smart elderly care services, thereby improving the quality of life for the elderly. Under effective policies and regulatory mechanisms, the smart elderly care industry can achieve a certain level of stability. The results of this study contribute to the advancement of the smart elderly care sector and provide a critical theoretical foundation for the construction of a smart elderly care service system.
• Select
  The Impact of Extreme Weather on the Volatility Spillover of Regional Financial Risk in China

  DONG Minghua, CHU Chengpei, WANG Jianli

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1106-1130. https://doi.org/10.12341/jssms240686

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  The increasing occurrence of extreme climate events poses a major threat to regional financial systems. Thus, exploring its impact mechanism is vital for preventing systemic financial risks. In this study, a comprehensive index analysis method and a DY variance decomposition matrix are used to calculate the regional financial risk volatility spillover values of 31 provinces, municipalities and autonomous regions selected in China from 2014-2022. Three climate proxy indicators are constructed for a balanced panel regression to measure their impact on those spillover values. The findings show that extremely high temperatures have a significantly positive association with spillover, while extremely low temperatures and extreme precipitation have no significant effect. Analyzing regional heterogeneity reveals that regions like Inner Mongolia, Xizang, and Northwest China, with lower economic development levels and more homogeneous industrial structures, are more vulnerable to spillover from extreme climate shocks. Moreover, regional carbon emission intensity positively impacts the relationship between extreme high temperatures and spillover. Strengthening regional carbon reduction mechanisms is key to mitigating the effects of extreme high temperatures on spillover. In conclusion, enhancing regional governments' awareness to prevent extreme climate shocks and strengthening carbon reduction mechanisms are crucial for addressing risks from extreme climate events.
• Select
  Channel Trade-Offs for Manufacturers Under Revenue-Sharing Contracts: Traditional Retailers vs.B2P Sharing Platforms

  YE Fei, ZHENG Kaiming, NI Debing

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1131-1148. https://doi.org/10.12341/jssms240377

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Based on the observation of the reality that brand manufacturers use revenue-sharing contracts to expand B2P (business-to-peer) sharing platforms as new sales channels, this paper establishes a dynamic game model that incorporates the strategic interaction between a manufacturer, a traditional retailer, and a B2P sharing platform, and reveals the impact of revenue-sharing ratios on the channel decisions of manufacturers (between traditional retail channels and B2P sharing platform channels) and the profitability of each player, based on the corresponding equilibrium outcomes. The results show that: 1) When the product usage rate is too low or too high, the revenue-sharing contract has no effect on the channel choice of the manufacturer. However, when the product usage rate is at a medium level, the revenue-sharing contract will affect its channel choice. In this case, there exists a revenue-sharing ratio threshold, and when the revenue-sharing ratio is higher than this threshold, the optimal channel choice for the manufacturer is a single B2P sharing platform channel; otherwise, the optimal channel choice is a dual channel. 2) The revenue-sharing ratio threshold increases in product usage rate but decreases in production costs and the platform's service level. 3) When the revenue-sharing contract affects the channel trade-offs, an increase in the revenue-sharing ratio will increase the manufacturer's profit, reduce the B2P platform and retailer's profits, and have a non-monotonic impact on the overall profit of the supply chain.
• Select
  The Nonlinear Impact of Digital Inclusive Finance on the Operating Performance of Regional Commercial Banks—Extrusion Effect or Spillover Effect

  CONG Yuyue, YU Zhongfu, YANG Ying, CHAI Jian

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1149-1166. https://doi.org/10.12341/jssms240464

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  This paper examines the impact of digital inclusive finance on the operational performance of regional commercial banks using a fixed-effects model based on balanced panel data from 78 urban and rural commercial banks spanning from 2011 to 2021. The results indicate a significant negative relationship between the two. This conclusion remains valid after addressing endogeneity issues and conducting robustness tests, suggesting that the current competitive crowding-out effect still exerts a substantial influence. Further analysis through moderation and threshold effects reveal that the technology spillover effect of digital inclusive finance drives business innovation and enhances risk-taking capacity among regional commercial banks, thereby mitigating their negative effects, with the moderation effect on risk-taking being more pronounced. The threshold parameter estimates show that business innovation has a more significant negative convergence moderation effect on rural commercial banks, while risk-taking exhibits a more significant negative convergence moderation effect on urban commercial banks. The findings of this study provide important practical insights for the digital transformation of regional commercial banks and the sustainable and healthy development of regional economies.
• Select
  Improved Multi-Objective Variable Neighborhood Search Algorithm for Aircraft Sequencing with Interdependent Runways

  CHEN Kejia, SITU Tengkuan, LIN Hongxi

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1167-1184. https://doi.org/10.12341/jssms240527

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Aiming at the multi-objective aircraft sequencing problem with interdependent runways, an improved multi-objective restart variable neighborhood search algorithm is proposed. An initialization method based on rolling and swap is proposed, which considers the impact of multiple flights on the solution when constructing the initial solution, increasing the probability that the initial solution jumps out of the local optimum. A variable neighborhood search strategy based on neighborhood delay feedback is designed. The adjusted flights and adjustment strategies are selected based on the delays near the flight, which improves the search speed and local search depth of the algorithm, and adds a restart operator to avoid premature algorithm convergence. Finally, through 30 public examples at different scales, the proposed algorithm is compared with the existing algorithms for aircraft sequencing such as explorative perturbative search, iterated simulated annealing, NSGA-II and receding horizon control strategy combined with simulated annealing and large neighborhood search, the inverted generational distance and hypervolume ratio of the solution set are better, which verifies the superiority and stability of the proposed algorithm for multi-objective aircraft sequencing.
• Select
  Cloud Alliance Dynamic Rewarding and Penalizing Trust Evaluation Approach Based on the Flexible Reference Solution

  PENG Dinghong, SONG Bo

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1185-1204. https://doi.org/10.12341/jssms240511

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  To effectively address and alleviate the trust uncertainty crisis faced by cloud service providers (CSPs) and cloud service consumers (CSCs) during the formation and adoption of cloud alliances, and to avoid incurring additional trust costs, it is essential to monitor and constrain the trust levels within these alliances in real time. For this reason, a dynamic trust evaluation approach for cloud alliances based on the flexible ideal solution ($FIS$) and reflecting reward-penalty mechanisms is proposed. The approach employs hesitant fuzzy elements (HFE) to integrate the different trust performances of CSPs in the alliance, providing a comprehensive and accurate characterization of the trust levels. Additionally, it introduces the COWA operator and hesitant fuzzy linguistic quantifiers to construct the $FIS$ and carries out the evaluation based on the idea of two $FIS$ as the theoretical basis. Furthermore, three distinct measurement approaches that reflect dynamical rewarding and penalizing for alliance trustworthiness (i.e. $TD$ and $UD$) are provided to meet practical decision-making needs. Finally, the applicability of the proposed dynamic evaluation method is validated through its application to a case study involving the selection of alliance partners for an internet company. Discussion on the impact of the varying absolute-relative inclination coefficients on the generation of FIS is presented, demonstrating the method's flexibility and superiority.
• Select
  Research on the Construction of New Energy Vehicle Battery Swapping Stations Based on Battery Discount and Battery Concession Contracts

  MA Xiuyan, XIE Lili, CAO Jian

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1205-1225. https://doi.org/10.12341/jssms240409

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  The construction of battery swapping stations supports the promotion of the “vehicle-electricity separation” model for new energy vehicles, and it is crucial to design a contract mechanism to encourage supply chain enterprises to jointly participate in the investment of battery swapping stations. This article studies the joint decision-making problem of investment and product pricing in new energy vehicle supply chain enterprises under different power structures, designs two models about battery price discount contracts and battery price concession contracts based on the number of battery swapping stations invested, and analyzes the impact of correlation coefficients on the decision-making of all parties. Research has shown that both battery price concession contracts and battery price discount contracts can make the supply chain achieve Pareto improvement; Under different power structures, either battery enterprise or car enterprise investing in the construction of battery swapping stations is beneficial for promoting the battery swapping model and increasing the profits of both enterprises; The construction cost of battery swapping stations significantly affects the investment willingness and pricing decisions of battery and car enterprises. The research results provide cooperative ideas and new contractual mechanisms for enterprises to make investment decisions in replacement power plants.
• Select
  Outsourcing Cooperation and Brand Spillover Strategy within Coopetitive Supply Chain

  YOU Guanzong, LUO Chunlin, JIANG Weifan, ZHANG Chenxi

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1226-1239. https://doi.org/10.12341/jssms240745

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Manufacturers may engage in outsourcing cooperation with suppliers during production while simultaneously competing with them in sales. When consumers exhibit a preference for a particular component or brand, the other party can promote its own product sales by advertising the partnership, thereby implementing a brand spillover strategy. Considering the scenarios of component brand spillover or product brand spillover, this study examines how the supplier's cost advantage, the manufacturer's product advantage, and the level of brand spillover affect the manufacturer's outsourcing decisions, and how these, in turn, influence brand spillover strategies within the supply chain. The research provides a reference for firms in formulating their marketing strategies. The findings indicate that: 1) In the case of component brand spillover, brand spillover may result in wholesale prices exceeding the manufacturer's costs, and the equilibrium in the supply chain will always favor brand spillover; 2) In the case of product brand spillover, brand spillover may lead to wholesale prices falling below the manufacturer's costs. The implementation of a brand spillover strategy within the supply chain requires consideration of factors such as the influence of both parties and differences in production costs; 3) Suppliers do not always benefit from an increase in the manufacturer's cost disadvantage.
• Select
  Existence and Stability of Strong Pareto-Nash Equilibria for Multi-Objective Population Games

  YUAN Linqing, JIANG Mengting, ZHANG Yu

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1240-1250. https://doi.org/10.12341/jssms241016

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  With the aim of maximizing any objective payment of populations, the concept on strong Pareto-Nash equilibrium of multi-objective population game is introduced. By utilizing the Ky Fan section theorem, under the continuity of the vector payment function and a cone properly quasi-concave assumptions, the existence theorem of the equilibrium is obtained. Meanwhile, the equivalent relationship between the strong Pareto-Nash equilibrium of multi-objective population games and the solutions of vector strong variational inequality problems is established. Applying the equivalent relationship of the equilibrium, the stability of the strong Pareto-Nash equilibrium in multi-objective population games is studied. Finally, corresponding examples are presented to explain results obtained in this paper in detail.
• Select
  Optimality Conditions and Relaxation Methods for Multi-Objective Optimization Problems with Switching Constraints

  LI Wenhao, LI Gaoxi

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1251-1268. https://doi.org/10.12341/jssms240916

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  For multi-objective switching constraint optimization problems, the presence of switching constraints can render the Karush-Kuhn-Tucker (K-K-T) conditions potentially invalid at feasible points. Therefore, it is necessary to investigate weaker stability concepts and applicable optimality necessary conditions. This paper first defines the generalized Guignard constraint qualification for such problems. Under this constraint qualification, we then construct and prove the necessary conditions for optimality. Due to the possible discontinuity of the feasible region in switching constraint programming problems, traditional nonlinear programming methods are difficult to apply directly. Finally, we propose a relaxation model for this problem and prove that, under certain assumptions, The Pareto efficient solution set and the Pareto weakly efficient solution set of the relaxation model converge to the Pareto efficient solution set and the Pareto weakly efficient solution set of the original problem in the sense of Kuratowski-Painlevé respectively. Additionally, the Pareto KKT set of the relaxation model converges upwards to the set of Pareto weakly stable points of the original problem.
• Select
  Approximate Strong Karush-Kuhn-Tucker Condition for Multi-objective Fractional Programming Problems

  DENG Xin, YANG Yingxue, TANG Liping

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1269-1277. https://doi.org/10.12341/jssms240801

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we introduce an approximate strong Karush-Kuhn-Tucker (ASKKT) condition in response to smooth multi-objective fractional programming problems. In such problems, we obtain ASKKT-type necessary and sufficient optimality conditions at efficient solution. We also give the sufficient condition of ASKKT condition for Geoffrion properly efficient solution. Furthermore, we give the relation between ASKKT and classical SKKT conditions.
• Select
  Research on the Operation Decision of Electric Vehicle Charging Service Based on Differential Game Model

  WANG Xiangyu, LI Keqiang, SUN Ting, TIAN Qiong, LIU Peng, WANG Pengfei

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1278-1294. https://doi.org/10.12341/jssms240529

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Focusing on the supply side of vehicle charging service, this study proposes two differential game models for charging pile operation decision-making, with the government, operator, and third-party platform (hereinafter referred to as the platform) as the participants. The two differential game models are decentralized (i.e., operators and platforms aim to maximize their own interests) and centralized (i.e., operators and platforms aim to maximize the overall interests of both). The results show that under the equilibrium state with fixed revenue distribution ratios between operator and platform, compared with the decentralized decision-making mode, the centralized decision-making mode can improve the efforts of operator and platform, service quality and social benefit. When the platform is relatively weak and has a lower share of revenue, adopting the centralized decision-making mode can achieve a Pareto improvement in the revenues of both operator and platform; conversely, when the platform is relatively strong and has a higher share of revenue, adopting the decentralized decision-making mode can increase the revenues of both operator and platform. This indicates that as platform develops from weak to strong, the decision-making mode of the charging service market may shift from centralized to decentralized. At this time, the proportion of government policy support will increase, and social benefit and service quality may decrease.
• Select
  An Automatic Coding Method for Open-Ended Questions in Survey

  WANG Feifei, WANG Liqiong, ZHAO Zimeng, JIANG Yan

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1295-1310. https://doi.org/10.12341/jssms240877

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Open-ended questions within surveys, devoid of predetermined response options, afford respondents greater latitude in articulating individual perspectives, thereby facilitating researchers' comprehension of respondents' stances on intricate matters and fostering the exploration of novel avenues for inquiry. Consequently, undertaking systematic investigations into these questions is deemed essential. Currently, the research method of open-ended questions in academia relies on manual coding based on Grounded theory. However, the preliminary stage of summarizing and sorting materials is laborious and time-consuming. Although there are guiding coding standards, there is no mature method to automate the process, which limits the scope of academic research. To address this challenge, our research proposes a new topic model method inspired by BERTopic to automate the coding of open-ended questions in questionnaires. We use Sentence BERT to embed documents, hierarchical clustering to cluster them, and Text Rank and PEGASUS to extract keywords and automatically summarize them. Our method can conduct hierarchical topic modeling on the input open-ended answer text, and achieve classic three-level coding. It can also obtain different numbers of themes at different levels to suit various needs. After applying our method on the open-ended question dataset of the government environmental impact assessment questionnaire, it can identify hierarchical themes with clear meanings, showing excellent results and significantly improving the efficiency of manual coding.
• Select
  Online Outlier Detection Method for Data Streams

  PENG Yijian, TIAN Mengxin, JU Yuanyuan, WU Liucang

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1311-1324. https://doi.org/10.12341/jssms240359

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  With the continuous development of Internet technology, data streams have been attracted wide attention. However, outlier may adversely affect the statistical inference of these data streams. So it is very important to study effective outlier detection methods. Because of the real-time characteristics, traditional outlier detection methods for data streams have been encountered challenges. To address this challenge, an online outlier detection method suitable for data streams are proposed in this paper. Firstly, the sample mean function of the data streams are updated online, and the principal component scores are updated to obtain the least trimmed scores set and evaluate the robustness of its mean estimator.Secondly, threshold rules are constructed based on the asymptotic distribution of distance to detect outlier, and one-step reweighting procedure is presented to control the false positive rate of outlier detection. Finally, the rationality and validity of the proposed method are verified by simulation and example analysis.
• Select
  Accuracy Enhancement of Aggregate Inverse Mean Estimation—Based on Improved Reweighting Method

  WANG Wenying, LI Wenjuan, CHEN Fei

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1325-1342. https://doi.org/10.12341/jssms240462

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  The aggregate dimension reduction (Wang et al, 2020; Wang and Yin, 2021) is a class of important approaches of sufficient dimension reduction, which have competitive advantages in handling complicated models. It conducts the dimension reduction in the $k$ neighborhood of each sample point and aggregate their results. In this paper, we try to adjust the distributions of data in the local areas to make them close to elliptical contoured distribution, which can improve the results of the local dimension reductions and enhance the accuracy of the final aggregate inverse mean estimate. However, because the sample size of the local areas cannot be large, the existing reweighting method based on the Voronoi weights (Cook and Nachtsheim, 1994) may be faced with two problems: Firstly, it may be difficult to construct the objective distribution fitting the data well; Secondly, it may be also difficult to obtain the weights of the data points. To solve these issues, we propose an adaptive reweighting method, which obtains the weights of the data points in each local area based on the result of an initial sufficient dimension reduction on it. We deduce several properties, revealing the relationship between the initial dimension reduction directions and the subspace on which the projection of the predictor vector does not satisfy the linear design condition, to illustrate the reasonableness of the proposed method. The proposed method is illustrated by simulations and a real data analysis.
• Select
  Longitudinal Data Modeling and Cluster Analysis Based on Growth Curve Mixture Model

  LI Rongli, FEI Yu

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1343-1364. https://doi.org/10.12341/jssms240356

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  The growth curve model is a classic model for longitudinal data analysis, which has two important assumptions: 1) The error matrix follows multivariate normal distribution; 2) The group matrix is known. In this paper, the above two assumptions are relaxed. Firstly, we extend the distribution of the error matrix from the multivariate normal distribution to the more general multivariate power exponential distribution, and discuss the parameter estimation of the model. Then we discuss parameter estimation of growth curve model with unknown group matrix (called growth curve mixture model). As a by-product, growth curve mixture model provides an analysis method for the clustering of longitudinal data. Simulation analysis and real data analysis show that the proposed method is effective and reasonable.
• Select
  Maximum Projective Stratification Enumerator for Space-Filling Designs

  WANG Dongying, HOU Mengda, ZHOU Qi

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1365-1381. https://doi.org/10.12341/jssms240814

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Computer experiment is widely used in scientific researches and engineering designs. It often involves a large number of factors at the early stage, thus space-filling design with good low-dimensional space-filling property is essential to identify the active factors. Researchers proposed the projective stratification pattern (PSP), based on the effect sparsity and effect hierarchy principles, to quantify the stratification when a design is projected into one dimension to full dimensions, and effectively select designs with good low-dimensional space-filling property. But for large-scale experiments, it requires massive computation.In this article, we propose a computationally efficient metric for PSP, called maximum projective stratification enumerator.The enumerator is proved to be a linear combination of PSP, and can be used to develop a rapidly calculating method for PSP.We also establish a lower bound and some relevant conclusions for the enumerator, and provide a flexible numerical algorithm for constructing designs with maximum projective stratification.
• Select
  Best Subset Selection Based on Smoothed Quantile Regression

  DONG Yu, GUO Chaohui

  Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1382-1394. https://doi.org/10.12341/jssms240990

  Abstract & Html ( ) Download PDF ( )   Knowledge map   Save

  Best subset selection can accurately and efficiently mine important information from high-dimensional data to build a reduced regression model. In recent years, it has been used more and more in machine learning, image processing and biomedicine. However, most of the existing optimal subset selection methods are based on least squares or maximum likelihood, resulting in insufficient robustness when dealing with heterogeneous data. In order to effectively deal with the heterogeneity of high-dimensional data and comprehensively analyze the conditional distribution of response variable, a robust optimal subset selection algorithm based on $\ell_{0}$ penalty and smoothing quantile loss function is designed in this paper. In practice, the real number of important variables is usually unknown. In this paper, a truncated sequential search algorithm is proposed for efficient and accurate selection of the number of important variables. In the simulation, comparing with the existing variable selection methods, it is found that the proposed method has more advantages in variable selection and parameter estimation accuracy.Finally, the new method is used to analyze the gene data related to the production of riboflavin by Bacillus subtilis. The experimental results show that the new method has a smaller quantile prediction error in estimating the riboflavin production rate.