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Off-site investment relations among enterprises often bring the flow of capital, logistics, talent, information, and technology across cities, representing a new avenue for studying the urban network. Therefore, an increasing number of studies are investigating urban networks from the perspective of firm relations. Most of these studies mainly use data from intra-firm branches or mega firms' investment to quantify the linkages among cities. However, these studies have neglected the linkages among small-sized enterprises that are often located in small and medium-sized cities, resulting in the lack of authenticity in establishing urban networks. Recently, a small amount of research has begun to use wholesale enterprises' off-site investment data to construct urban networks. However, such research has neglected the indirect linkages and transit effects on enterprise investment routes. Therefore, this study uses investment data of all-industry enterprises from the Industrial and Commercial Enterprise Registration Database to propose a new method for establishing a directed weighted urban network by identifying off-site investment routes among enterprises, which could fill the gap in constructing urban networks from the perspective of micro capital flow. To verify the evolutionary characteristics of urban network structure before and after the implementation of major policies, this study considers the Yangtze River Delta as the empirical study area. Wholesale enterprise investment data from 2006 to 2020 in the Yangtze River Delta are used to construct three urban networks in three time stages. The main conclusions are as follows: (1) The growth model of the urban network scale shows that the growth of off-site investment routes drives the growth of off-site investment scale. The scale of enterprise nodes linked by off-site investment relations significantly increased from 2011 to 2015. However, after 2016, the proportion of off-site investment in the total investment of the Yangtze River Delta increased accordingly. (2) From the perspective of spatial patterns, the urban network of the study area has shifted from a polygonal network structure of interconnected core cities to a V-shaped structure centered around Shanghai, and then to a Z-shaped structure centered around Shanghai and Hangzhou. (3) In terms of network centrality, the cities exhibit a clear hierarchical structure. Although the network is evolving, the hierarchical structure has not changed significantly. However, the linkages between cities show a trend of clustering from low- to high-level cities. (4) In terms of network betweenness, the betweenness of most cities matches their centrality. Notably, the betweenness of Hefei and Wuhu is significantly stronger than their centrality. At different stages of the urban network evolution, cities with high betweenness, such as Shanghai, Hangzhou, and Hefei, play different intermediary roles in the network. This study constructs urban networks from a micro scale perspective of capital flow, thereby filling the gap in existing research. Additionally, unlike previous studies on urban networks that focus on static network structures, this study analyzes the structural evolution of urban networks based on long-term comprehensive data and verifies the characteristics of changes in the network structure, which has certain theoretical value and practical significance.

With the development of science and technology, massive datasets stored in multiple machines are increasingly prevalent. It is known that traditional statistical methods may be infeasible for analyzing large datasets owing to excessive computing time, memory limitations, communication costs, and privacy concerns. This article develops divide‐and‐conquer empirical likelihood (DEL) and divide‐and‐conquer exponentially tilted empirical likelihood (DETEL) methods for the distributed computing setting. We investigate the theoretical properties of the DEL and DETEL estimators. In particular, we derive upper bounds for the mean squared errors of the DEL and DETEL estimators, and, under some mild conditions, we prove the consistency and the asymptotic normality of the proposed estimators. Simulation studies and a real data analysis are carried out to demonstrate the finite‐sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Pareto distributions are useful for modeling the loss data in many fields such as actuarial science, economics, insurance, hydrology and reliability theory. In this paper, we consider the simultaneous estimation of the risk parameters of Pareto distributions from the perspective of empirical Bayes, novel SURE-type shrinkage estimators are developed by employing the Stein's unbiased estimate of risk (SURE). Specifically, due to the lacking of the analytic form for the risk function, we propose to estimate the hyperparameters by minimizing an unbiased estimate of an approximation of the risk function. Under mild conditions, we prove the optimality of the new shrinkage estimators. The performance of our estimators is illustrated with simulation studies and an analysis of a real auto insurance claim dataset. [ABSTRACT FROM AUTHOR]

Clustering is an important task in statistics and many other scientific fields. In this note, we propose an improved K-means clustering approach called 'enhanced shrinkage K-means' based on the James-Stein estimator and learning vector quantization (LVQ) algorithm. The basic idea of this new algorithm is taking into account of the strength of both unsupervised clustering and supervised classification methods, in which we shrink the clustering centers toward the prototype vector via James-Stein estimator. We carry out extensive simulation studies and real data analysis to evaluate the performance of this new approach, and obtain encouraging results. [ABSTRACT FROM AUTHOR]