It is of great significance to understand the spatial non-equilibrium and the solidification degree of transportation carbon emissions, so that differentiated measures can be taken to reduce transportation carbon emissions. Based on China's provincial data from 2005 to 2015, this article uses the Dagum Gini coefficient to decompose the spatial non-equilibrium of per capita transportation carbon emissions from static viewpoint. The results indicate that the overall spatial non-equilibrium shows a significant downward trend; the intensity of transvariation has had an increased contribution rate year by year since 2008, and replaces the inter-regional differences as the main source of the overall spatial non-equilibrium. Next, Kernel density estimation is employed to analyze the evolution laws of spatial non-equilibrium from dynamic viewpoint. The results show that the per capita transportation carbon emissions in the eastern region are successively higher than those at the national level, and in other regions. Meanwhile, some provinces are concentrated at a low level, while others at a high level. Finally, Markov chains approach is applied to identify the solidification effect of the spatial non-equilibrium. The results indicate that the effect is obvious and the state transitions occur only between adjacent types. Moreover, the solidification effects of the provinces with higher per capita transportation carbon emissions are stronger than those provinces with a lower level.

Credit scoring is one of the key problems in financial risk managements. This paper studies the credit scoring problem based on the set-valued identification method, which is used to explain the relation between the individual attribute vectors and classification for the credit worthy and credit worthless lenders. In particular, system parameters are estimated by the set-valued identification algorithm based on a given recognition criteria. In order to illustrate the efficiency of the proposed method, practical experiments are conducted for credit card applicants of Australia and credit card holders from Taiwan, respectively. The empirical results show that the set-valued model has a higher prediction accuracy on both small and large numbers of data set compared with logistic regression model. Furthermore, parameters estimated by the set-valued identification method are more stable, which provide a meaningful and logical explanation for extracting factors that influence the borrowers’ credit scorings.

In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders’ future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown theoretically that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cramér–Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms.

In this paper, we investigate a credit rating problem based on the network of trading information (NoTI). First, several popular tools, such as assortativity analysis, community detection and centrality measurement, are introduced for analyzing the topology structures and properties of the NoTI. Then, the correlation between the characteristics of the network and the credit ratings is investigated to illustrate the feasibility of credit risk analysis based on the NoTI. Sovereign rating based on the world trade network is analyzed as a case study. The correlation between the centrality metrics and the sovereign ratings conducted by Standard & Poor's clearly shows that highly ranked economies with vigorous economic trading links usually have higher credit ratings. Finally, a simulation is conducted to illustrate the degree of improvement in credit rating prediction accuracy if the NoTI is considered as an additional attribute.

This paper studies an average consensus problem for multi-agent systems (MAS) with binary-valued communications of relative state between neighbors. A two-scale algorithm consisting of 'estimation' stage and 'control' stage is proposed for discrete-time MAS over directed graph. In the 'estimation' stage, the relative states between agents and neighbors are estimated with and without considering measurement noise. In 'control' stage, a distributed control protocol is designed based on the estimations of relative states to achieve average consensus. Convergence and convergence speed of the algorithm are analyzed theoretically under mild conditions. Finally, a numerical simulation is given to validate the developed results of this paper.

In this paper,  the credit scoring problem is studied by incorporating network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide a prediction for lenders assuming that published credit scores are estimated merely from structured individual data. Such prediction is used as a monitoring indicator for the risk warning  in lenders' future financial decisions. Secondly, we further propose a recursive Bayes estimator to improve the accuracy of credit scoring estimation by incorporating the dynamic interaction topology of clients as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cram\'er--Rao lower bound for clients within a certain range of scores. Finally, simulation results for a specific case illustrate the effectiveness and feasibility of the proposed methods.