中国科学院数学与系统科学研究院期刊网

09 June 2026, Volume 46 Issue 6
    

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  • WANG Yi, DU Juan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1757-1775. https://doi.org/10.12341/jssms240800
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    In response to the fact that existing environmental performance evaluation methods are mostly based on the optimistic frontier constituted by efficient decision-making units, this study introduces the concept of double frontier evaluation into the directional SBM model, proposes a new double frontier directional SBM model considering undesirable output, and develops its super efficiency expression to improve the model's ability to distinguish decision-making units. This method evaluates environmental performance from both optimistic and pessimistic frontier perspectives, while simultaneously accounting for potential biases introduced by improvement directions and slacks, effectively strengthening the recognition of the evaluation results among all participants. On this basis, a global Malmquist index satisfying the circular test based on the double frontier directional SBM model is constructed to accurately measure the dynamic evolution of environmental performance across provinces in China from 2011 to 2021. The results indicate that China's green total factor productivity shows a fluctuating upward trend, with technological progress identified as the principal driver. Significant regional heterogeneity is observed in technological efficiency changes among different economic zones. This study is important for the continuous improvement of green total factor productivity in regions according to local conditions, as well as for the orderly advancement of the carbon peaking and carbon neutrality goals.
  • LUAN Liyuan, WU Fei, GUO Kun
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1776-1794. https://doi.org/10.12341/jssms240625
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    To analyze risk contagion characteristics across commodity futures in China, this study employs a multi-layer network approach to construct a risk spillover network model that captures both normal market conditions and extreme upward/\linebreak downward market scenarios. The research conducts an in-depth investigation of risk transmission patterns within China's commodity futures market under varying market states. Static network analysis confirms the significant risk aggregation effects observed across commodity sectors in different market conditions, revealing energy and chemical commodities as primary risk transmitters under normal circumstances, while metal sector commodities exhibit greater prominence during extreme market states. Dynamic network analysis uncovers temporal evolution in market structures and their responses to major events, demonstrating that significant external shocks alter the risk transmission architecture of commodity futures markets. The findings further indicate that negative shocks enhance the inter-connectivity of risk information transmission within market structures, thereby intensifying risk contagion effects. Additionally, the study identifies key nodes that retain structural importance in risk contagion across different market states, providing critical insights for understanding and predicting market regime transitions. These findings offer valuable implications for investor behavior and risk management strategies, deepen the comprehension of systemic risk propagation in China's commodity markets, and establish an empirical foundation for formulating effective risk management protocols and regulatory frameworks. The methodological framework presented contributes to the advancement of financial network analysis in commodity market research.
  • NI Xuanming, SUN Xueyuan, NI Jihang, LIU Yixuan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1795-1810. https://doi.org/10.12341/jssms250723
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    Amidst global economic uncertainties and domestic structural transitions, bolstering corporate investment efficiency stands as a pivotal driver for China's high-quality economic evolution. In April 2024, the Political Bureau of the CPC Central Committee first proposed nurturing “patient capital”——A capital form defined by long-term commitment, elevated risk tolerance, and strategic relational attributes, which aligns seamlessly with enterprises' pursuit of sustainable, high-quality growth. This study empirically examines the impact of patient capital on corporate inefficient investment, utilizing a comprehensive dataset of Chinese A-share listed companies on the Shanghai and Shenzhen stock exchanges from 2008 to 2023. Our findings reveal that patient capital significantly mitigates both underinvestment and overinvestment, thereby enhancing investment efficiency. This positive effect is achieved through two key mechanisms: The resource mechanism, which facilitates the infusion of financial and business resources, and the governance mechanism, which strengthens corporate governance frameworks, internal controls, and external regulatory environments. Heterogeneity analysis uncovers that the efficacy of patient capital in curbing inefficient investment varies across firms with different technological capabilities, market competition intensities, and levels of fiscal support. By innovatively exploring patient capital from the perspective of corporate resource allocation, this research not only illuminates its critical role in optimizing investment efficiency, but also provides actionable insights for refining capital market structures and enhancing capital allocation. These findings offer strategic guidance for policymakers and corporate decision-makers aiming to elevate investment efficiency and drive high-quality economic development.
  • GUO Peiqiang, LI Zhiwen, XIA Peng, ZHOU Tai
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1811-1830. https://doi.org/10.12341/jssms250205
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    This study adopts a game-theoretic model to examine the strategic decisions of physical pharmacies regarding participation in a pharmaceutical platform that offers two delivery modes: Traditional non-technical delivery (NTD) and technical delivery (TD). A benchmark model is established to analyze the operational choices of pharmacies before and after joining the platform, focusing on drug variety, logistics pricing, and profitability under each delivery mode. The research results show that when the logistics distribution cost is low, physical pharmacies will choose to join the pharmaceutical platform. At this time, the TD mode provides more drug types than the NTD mode, and the overall profit is higher, so the TD mode should be adopted; When the logistics distribution cost is at a medium level, any of them can be adopted; When the logistics distribution cost is high, neither mode will be chosen. In addition, the number of physical pharmacies will not affect the types of drugs before joining the platform, and when the number of pharmacies is small, there is no obvious difference in the optimal profit between the two modes. However, when physical pharmacies join the medical platform, as the number of pharmacies increases, the TD model will gain more profits, and when larger physical pharmacies join the platform, it will be beneficial to both parties and can achieve Pareto improvement. By further exploring the competition among platforms, it can be found that competition will intensify the contradictions between platforms, thereby reducing both their individual and overall profits.
  • LEI Xiyang, MAO Chengyang, DAI Qianzhi, LIU Haoxiang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1831-1847. https://doi.org/10.12341/jssms240674
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    Improving energy and environmental efficiency is one of the effective means to achieve energy conservation and emission reduction in the transport system. It is worth noting that China's transport system is a parallel structure system consisting of freight transport subsystem and passenger transport subsystem. At the same time, there is an obvious game relationship between total systems in the process of efficiency evaluation. Therefore, this paper combines the non-cooperative game with data envelopment analysis (DEA) to propose a non-cooperative game DEA method considering parallel structure to measure the energy-environmental efficiency of the transport system. Firstly, this paper designs an optimal efficiency algorithm for the total system and proves the convergence of the algorithm and the uniqueness of the optimal solution. Then, a subsystem efficiency decomposition model is designed from the leader-follower perspective, and the existence of the solution of the efficiency decomposition model is further proved. Finally, the methodology of this paper is applied to the efficiency measurement of China's transportation system in 2022. The results indicate that 1) China's transportation system has low overall energy and environmental efficiency, with only six provinces having an efficiency of 1; 2) The energy and environmental efficiency of the transport system in the eastern region is better than that in the central and western regions, while the energy and environmental efficiency of the freight subsystems in the western region is slightly better than that in the central region; 3) The passenger transportation system generally has higher efficiency than the freight system. The results of the efficiency evaluation in this paper provide a direction and theoretical basis for the improvement of the energy and environmental efficiency of China's future transportation system.
  • LI Xiaofei, LÜ Shuang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1848-1866. https://doi.org/10.12341/jssms240582
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    Against the backdrop of rapid development in e-commerce and retail, market competition continues to intensify. Accurate sales forecasting and dynamic pricing have become critical tools for retailers to enhance operational efficiency, optimize resource allocation, and strengthen competitive advantage within a complex market environment. Concurrently, the digital transformation and intelligent upgrading of the retail industry are driving companies from traditional experience-based management towards data-driven scientific decision-making. Particularly for perishable goods, swiftly responding to market changes and adjusting prices are crucial for inventory management, waste reduction, and improving sales efficiency. Based on this, this paper proposes a retail forecast optimization and commodity classification dynamic pricing system, consisting of a high-precision forecasting subsystem and an intelligent pricing subsystem, aiming to achieve dual optimization of dynamic pricing and accurate sales forecasting. The high-precision forecasting subsystem constructs a hybrid model integrating Bidirectional Long Short-Term Memory (Bi-LSTM) and Bidirectional Gated Recurrent Unit (Bi-GRU), combined with Variational Mode Decomposition (VMD) technology, effectively capturing statistical patterns and trend fluctuations across different frequency sequences to realize high-accuracy multi-step forecasting of product sales and purchase prices; The intelligent pricing subsystem employs the IGWO-JAYA dynamic optimization algorithm to formulate dynamic pricing strategies for different categories, thereby maximizing revenue and achieving real-time market response. Results indicate that this system improves the prediction accuracy of product sales and purchase prices and can provide optimal pricing strategies for different categories of products, significantly enhancing retailers' adaptability to market changes and profit potential, supporting the intelligent development and efficiency improvement of the retail industry.
  • TAN Tao, LI Biao, WU Lijun, ZHOU Yong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1867-1886. https://doi.org/10.12341/jssms241041
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    In this paper, we consider three types of agents: Policyholders, insurers, and reinsurers. From the perspective of the insurer and the reinsurer, we measure the risk through the distortion risk measures. When the premium principle is the distortion premium principle, we obtain the optimal form of the loss function of the policyholder and the insurer respectively. The result shows that in some cases, the risks of the policyholder and the insurer need to be fully borne by the insurer and the reinsurer. In some cases, the risks of the policyholder and insurer do not need to be borne by the insurer and reinsurer. When the distortion risk measures is designated as value at risk (VaR) and tail value at risk (TVaR) risk measure, and the distortion premium principle is designated as the expected premium principle, we analyze the optimal reinsurance problem in detail, and give the optimal form of the loss function of the policyholder and insurer respectively under different circumstances.
  • LI Minchan, LING Liwen, ZHANG Dabin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1887-1900. https://doi.org/10.12341/jssms240567
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    Financial market prices are affected by many factors and exhibit complex characteristics such as nonlinearity, non-stationarity, and high dimensions, making trend prediction very difficult. In order to further improve the accuracy of trend prediction, this paper proposes a model based on time series image coding and convolutional neural network optimized by genetic optimization, referred to as CMIE-GA-CNN (combining multi image encoding-genetic algorithm-CNN). First, from the perspective of feature engineering, aiming at the problem of difficult representation of high-dimensional characteristics of financial time series, the one-dimensional time series is encoded into two-dimensional images such as Gram graph, recurrence graph, Markov diagrams and line charts extract their high-dimensional invisible features. Secondly, the above images are combined to overcome the information loss problem of single-type image encoding. Finally, a genetic algorithm is introduced to optimize the parameters of the convolutional neural network to improve the performance of the prediction model. The combined graph is used as input to obtain the prediction results. In order to confirm the effectiveness of the proposed model, trend prediction and turning point prediction are performed on three groups of financial time series: The Dow Jones Industrial Average Index, the S\&P 500 Index, and the U.S. Dollar Index, compared with common prediction methods, single-class image encoding input and deep learning prediction methods without parameter optimization, the model in this paper improves the trend prediction accuracy and is more robust.
  • LUO Suizhi, HU Sihuan, HE Xiaorong, CAI Mengsi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1901-1922. https://doi.org/10.12341/jssms240901
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    Online travel reviews encapsulate travelers' authentic experiences and serve as a crucial reference for potential tourists' decision-making. However, due to the vast number of reviews, it becomes challenging for potential tourists to browse each one and effectively extract valuable information. Moreover, existing research on travel itinerary recommendations often lacks sufficient sentiment analysis of online reviews, making it difficult to accurately reflect user needs. Considering that selecting a travel itinerary typically involves multiple constraints, this paper proposes a MACONT multi-attribute decision-making method based on picture fuzzy sets to recommend suitable travel itineraries for potential tourists. Firstly, we utilize the Octopus web scraping tool to collect travel itinerary review data from the Ctrip travel website and preprocess the text using Jieba for word segmentation. Subsequently, the LDA topic model is employed to identify decision attributes and their weights for travel itineraries. Next, SnowNLP sentiment analysis is applied to extract the sentiment orientation of the reviews, quantifying them into picture fuzzy numbers. Then, integrating the MACONT multi-attribute decision-making method, a picture fuzzy MACONT decision model is constructed to achieve a comprehensive ranking of travel itineraries. Finally, a case study is conducted to validate the proposed method's rationality, and further sensitivity and comparative analyses are performed to demonstrate its effectiveness.
  • YAN Hui, XU Yangdong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1923-1935. https://doi.org/10.12341/jssms240911
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    As a classical imprecise line search method in multiobjective optimization, the Armijo line search can fully guarantee the reduction of all objective functions. However, empirical results show that the Armijo line search often results in a very small stepsize along the steepest descent direction, which seriously prolongs the time required for the algorithm to converge. To address this limitation, this paper proposes a Barzilai-Borwein descent method for multiobjective optimization problems with weak Armijo line search. The stepsize updating in weak Armijo line search needs to satisfy all inequalities simultaneously, which makes it possible to reduce only one objective function value in some iterations. Thus, it is a nonmonotone line search. In addition, the convergence property of the algorithm is proved. Finally, numerical examples show that the multiobjective Barzilai Borwin algorithm with weak Armijo line search strategy significantly outperforms the existing ones with Armijo line search strategy and other nonmonotone line search strategies.
  • WU Meiying, GAO Jingying, YANG Wei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1936-1950. https://doi.org/10.12341/jssms250980
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    The traditional TOPSIS method frequently compromises the validity of evaluation outcomes when handling correlated assessment indicators, owing to distortions in the Euclidean distance between the evaluation subject and both positive and negative ideal solutions. Concurrently, as the dynamic nature of evolving phenomena imposes new demands upon evaluation methodologies, the limitations of conventional static assessment models become increasingly apparent. To address these issues, this paper introduces elastic net regression for indicator screening, constructing an entropy-weighted TOPSIS dynamic evaluation model based on elastic net regression. This model not only effectively handles highly correlated variables but also accommodates comprehensive evaluation needs within complex, continuously changing environments. Finally, using Chinese eight major comprehensive economic zones as a case study and comparing it with relevant models, the results demonstrate that the method achieves scientific screening and dynamic integration of highly correlated indicators. Moreover, it exhibits superior identification capabilities regarding efficiency structures and levels in empirical tests, demonstrating good applicability and practical explanatory power.
  • ZHOU Yufeng, PENG Jing, BAI Yun
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1951-1971. https://doi.org/10.12341/jssms241019
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    The study aims to develop a high-performance prediction model tailored to the blood collection and supply scenarios unique to China, considering its specific national conditions. It begins by analyzing seven factors: Workdays, holidays, weekdays, months, seasons, winter and summer vacations, and the blood collection volume from the previous day. Statistical analyses confirm that all these factors significantly influence daily blood collection volumes. Subsequently, the study proposes a CNN-LSTM hybrid model that integrates convolutional neural networks (CNN) and long short-term memory (LSTM) networks. The CNN component extracts periodic and local features from the data, while the LSTM component captures long-term temporal dependencies, enhancing feature representation capabilities. Experimental results demonstrate that the CNN-LSTM model outperforms other models, including CNN, LSTM, generalized regression neural network (GRNN), back propagation neural network (BPNN), extreme learning machine (ELM), seasonal autoregressive integrated moving average (SARIMA) and linear regression (LR). The CNN-LSTM model achieves the most comprehensive extraction of time series features across multiple factors and delivers the highest prediction accuracy. Specifically, its normalized mean absolute error (NMAE) and normalized root mean square error (NRMSE) are reduced by up to 25.80% and 26.54%, respectively, while the coefficient of determination ($R^2$) improves by up to 320.85%. The prediction results provide more precise decision-making references for blood collection and supply institutions, enabling better adjustment of collection plans and inventory management strategies.
  • WANG Ren, LUO Dan, XU Hao, LIU Ge, LIU Juan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1972-1995. https://doi.org/10.12341/jssms260036
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    Against the backdrop of accelerating digital and intelligent transformation in the current economy and society, cybersecurity has become a critical strategic issue with far-reaching implications. This paper constructs a combined risk management framework of “direct defense + cybersecurity insurance” to investigate optimal cybersecurity investment strategies for centralized and decentralized enterprises under uncertain losses. Breaking from existing research reliant on fixed loss distributions, this study adopts a data-driven approach. It constructs a high-dimensional loss uncertainty set based on Laplace kernel density functions and derives optimal solutions through robust optimization methods. Findings reveal: The strategies derived from this model exhibit greater robustness than traditional models; Compared to decentralized enterprises, centralized enterprises face fewer investment constraints and enjoy greater decision flexibility, with distinct investment strategies emerging between the two; When budgets are constrained, firms should select strategies aligned with their risk aversion levels. As budgets increase, firms exhibit a pattern of rising direct defense expenditures, insurance premiums, and wealth utility followed by stabilization. With ample budgets, firms should proactively opt for full insurance coverage. This paper provides theoretical foundations and practical guidance for firms to develop scientifically sound, practical, and effective cybersecurity defense strategies.
  • LUO Chunlin, WANG Biao, YOU Guanzong, LUO Mei, CHEN Qian
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 1996-2014. https://doi.org/10.12341/jssms250859
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    The rapid expansion of retailers' store brands and organizational restructuring toward independent business units have made the selection of store brand contract manufacturers a critical strategic decision. Based on a supply chain system comprising one manufacturer and one retailer, this paper develops a two-stage game-theoretic model to systematically compare equilibrium outcomes before and after division independence, as well as between sourcing from a brand manufacturer and a specialized contract manufacturer. It investigates how organizational restructuring influences the selection of store brand production partners. The findings reveal that regardless of whether a store-brand division is established, the retailer's optimal strategy is to select the brand manufacturer to produce the store brand when the products exhibit low substitutability. Under both organizational structures, there exists a possibility that dedicated contract manufacturer can achieve higher social welfare. The establishment of a store-brand division significantly reduces the probability of retailer choosing the dedicated contract manufacturer model, and strengthening the constraints imposed by contract manufacturing costs on this model. Under certain conditions, the establishment of business unit enhances consumer surplus and social welfare under both contract manufacturing models.
  • GUO Lishuo, SONG Xiaoyu, YAO Yeqi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2015-2033. https://doi.org/10.12341/jssms250019
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    Urban water supply infrastructure, as one of the critical systems in the urban lifeline framework, is essential for the normal functioning of cities. In the face of increasingly severe disaster risks, measuring and enhancing the resilience of water supply infrastructure is crucial. This paper follows the approach of characterizing the water supply infrastructure network and its service performance evolution, constructing a resilience model, and conducting case simulations. Two failure modes, namely instantaneous and progressive, are considered. A resilience measurement model based on the Sigmoid function is developed, focusing on a “node-link” framework. Case simulations are used to demonstrate that the proposed model can reflect the dynamic changes in the resilience of water supply infrastructure under different failure modes, and the impacts of risk shock coefficients, water transmission rates, and the duration of risk shocks on the resilience of water supply infrastructure are explored. The resilience measurement model established in this paper can help managers better understand the trends and sensitive factors affecting the resilience of water supply infrastructure, providing references for enhancing resilience in the face of risks. Furthermore, the theoretical framework for measuring infrastructure resilience has been expanded.
  • QU Tianyao, LIAO Xiou, JU Xiaohang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2034-2047. https://doi.org/10.12341/jssms240890
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    Model averaging is a hot issue in the field of statistics and econometrics. Many model averaging methods have been proposed and the statistical properties of corresponding weights have been verified. Multivariate model is an important statistical model, which is widely used in various fields. In this paper, the convergence rate of weights in the model average estimation is obtained in the sense of MMMA and MJMA based on the linear statistical model with multiple dependent variables, and the verification results also cover the convergence rate of the model average estimated weights in the case of single dependent variables. In addition, we verify the convergence rate of weights by corresponding numerical simulation.
  • ZHANG Peng, CHEN Wangxue
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2048-2063. https://doi.org/10.12341/jssms240884
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    This paper explores the characteristics of optimal estimation for the population variance $\sigma ^2$ in a normal distribution $N(\mu,{\sigma ^2})$, where $\mu$ is known, utilizing balanced ranked set sampling (RSS). The theoretical findings indicate that the balanced RSS estimation of population variance exhibits greater efficiency compared to the estimation derived from simple random sampling (SRS). To enhance the efficiency of statistical inference, we propose a Fisher information maximization approach and a quasi-sufficient complete statistic framework for the RSS design. Furthermore, we investigate the optimal estimation of population variance and analyze its characteristics under these two methodologies. The numerical findings indicate that the RSS estimation of population variance utilizing Fisher information maximization, as well as the RSS estimation based on quasi-sufficient complete statistics, exhibit superior efficiency compared to the balanced RSS estimation. Furthermore, the quasi-sufficient complete statistic RSS estimation for population variance demonstrates greater efficiency than that derived from Fisher information maximization. Furthermore, this paper explores the characteristics of optimal estimation for the population variance $\sigma ^2$ in a normal distribution $N(\mu,{\sigma ^2})$, where $\mu$ is unknown, utilizing balanced RSS. The numerical findings indicate that the balanced RSS estimation of population variance exhibits greater efficiency compared to the estimation derived from SRS when $\mu$ is unknown. The real data analysis is provided to illustrate the numerical findings.
  • WEI Shuhao, YANG Yufei, YU Jiani, HUANG Hengzhen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2064-2077. https://doi.org/10.12341/jssms241069
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    An order-of-addition experiment is a scientific experiment where the experimental result is affected by changing the addition order of components. This paper considers the order-of-addition experiment with conditional effects, i.e., the situation where a specific component $k$ needs to be added before another specific component $l$.By using the general equivalence theorem, we first prove the optimality of the full design based on the order-of-addition model with conditional effects. It is found that the design structure of the order-of-addition with conditional effects under the pairwise-order model has a similar relationship with the structure of the order-of-addition orthogonal array of strength $3$.Therefore, optimal fractional designs of the order-of-addition with conditional effects can be constructed based on order-of-addition orthogonal arrays of strength $3$. The usefulness of the design and model is demonstrated using a single machine scheduling problem.
  • ZHENG Renjing, DONG Yinshuang, HU Guihua, QI Li, WU Di
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2078-2095. https://doi.org/10.12341/jssms240658
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    This paper aims to improve estimated precision of total number of the population and net census error by means of triple system estimator on the basis of the census list, post-enumeration survey list, and administrative record list. In order to realize this goal, the triple system estimator and its related questions are studied through mathematical model. The research shows that the triple system estimator can not be constructed and used in the population directly; The triple system estimator is a biased estimator, its sample variance, bias, and squared error should be calculated. The triple system estimator will produce main role in the future of net census error estimation, which will gradually replace the widen used dual system estimator including correlation bias.
  • LI Qiang, SHI Huijun, HE Daojiang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(6): 2096-2108. https://doi.org/10.12341/jssms240589
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    The generalized $\log$-Moyal (GLM) distribution, as a new class of heavy-tailed distribution, is closely related to the Moyal distribution, half-normal distribution, and $\chi^2$ distribution. In this paper, the authors adopt the objective Bayes method to make statistical inferences for its parameters. Firstly, some noninformative priors, including the probability matching prior, Jeffreys prior, reference priors and maximum data information (MDI) prior, are derived, where it is shown that the reference prior is a probability matching one. Secondly, the posterior propriety based on the Jeffreys prior, reference prior and MDI prior is validated, where it is shown that the posterior distributions under the three priors are all proper. The simulation study demonstrates that the proposed Bayes method offers several advantages over the maximum likelihood method. Finally, the proposed Bayes method is applied to analyze a real data set.