Adaptive cluster sampling (ACS) is an efficient sampling technique for studying populations where the characteristic of interest is rare or spatially clustered. This method is widely applied in fields such as ecological studies, epidemiology, and resource management. ACS initially selects sampling units using simple random sampling without replacement. However, in some cases, selected networks may overlap, leading to multiple networks being included in the sample. To address this issue, a modified version of ACS was developed to ensure sampling without replacement at the network level, maintaining sampling symmetry and preventing the inclusion of overlapping networks. Despite this adjustment, asymmetry may still occur when network formation is highly irregular. This issue can be mitigated by incorporating auxiliary variables, which help correct distortions in the sampling process. In many situations, auxiliary variables related to the variable of interest can be utilized to enhance the precision of population parameter estimates. This research proposes multiplicative generalization for an estimator with two auxiliary variables using adaptive cluster sampling with networks selected without replacement. The bias and mean square error (MSE) are derived using a Taylor series expansion to determine the optimal conditions for minimizing MSE. A simulation study is conducted to support the theoretical findings. The results show that the proposed estimator under the optimal values of $T_1$ and $T_2$ is the most efficient to minimize MSE.

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary variable information to improve estimation efficiency. These estimators were developed using the jackknife resampling technique to improve the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), were derived, and a simulation study was conducted to validate the theoretical findings. The results demonstrated that the proposed estimators consistently outperformed conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibited superior efficiency to existing ratio estimators that do incorporate auxiliary information.

With the growing global emphasis on sustainable development goals, Environmental, Social, and Governance (ESG) factors have emerged as critical considerations in shaping economic policies and strategies. This study employs the ARMA-eGARCH-skewed t and Vine Copula models, combined with the CoVaR method, to investigate the dependence structure and risk spillover pathways across various industrial sectors in China within the ESG framework. By modeling the complex interdependencies among sectors, this research uncovers the relationships between individual industries and the ESG benchmark index, while also analyzing the correlations across different sectors. Furthermore, this study quantifies the risk contagion effects across distinct industries under extreme market conditions and maps the pathways of risk spillovers. The findings highlight the pivotal role of ESG considerations in shaping industrial structures. Empirical results demonstrate that industries such as agriculture, energy, and manufacturing exhibit significant systemic risk characteristics in response to ESG fluctuations. Specifically, the identified risk spillover pathway follows the sequence: agriculture → consumption → ESG → manufacturing → energy. The CoVaR values for agriculture, energy, and manufacturing indicate a significant potential for risk contagion. Moreover, sectors such as real estate, finance, and information technology exhibit significant risk spillover effects. These findings offer valuable empirical evidence and a theoretical foundation for formulating ESG-related policies. This study suggests that effective risk management, promoting green finance, encouraging technological innovation, and optimizing industrial structures can significantly mitigate systemic risks. These measures can contribute to maintaining industrial stability and fostering sustainable economic development.

The signing and implementation of Regional Comprehensive Economic Partnership (RCEP), being one of the largest free trade agreements, had multifaceted impacts on the participating countries. In the realm of regional economic cooperation, it has strengthened cross-border trade and collaboration, fostering increased economic integration and providing nations with more opportunities for economic growth. In the financial sector, financial cooperation has deepened, and the interconnectivity of stock markets among countries has grown. While aiding collective responses to financial crises and challenges, it has also created conditions for the contagion and spread of financial risks. This study utilized time-series data of stock indices from member countries in RCEP to examine the dependence structure. Initially, the study measures the volatility effects of stock markets using Ljung–Box test and then employed an ARMA-EGARCH model to filter time series data of stock indices. And then we obtained the marginal distributions of each variable from the standardized residuals. For joint distribution, We constructed a Vine Copula model to analyze the dependence structure. Comparing the \(\tau\) of Vine Copula through pre-RCEP and post-RCEP implementation, we found that RCEP enhanced stock market linkages among member countries. Meanwhile, the implementation of the RCEP has altered the dependence structure among the member countries. South Korea has emerged as a central node within this structure, while Japan’s position has been overtaken by Australia. This indicates that RCEP has exerted a notable influence on the financial markets of its member countries, a shift that has been effectively captured by the Vine Copula model.

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary variable information to improve estimation efficiency. These estimators are developed using the Jackknife resampling technique, which is employed to enhance the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), are derived, and a simulation study is conducted to validate the theoretical findings. Results demonstrate that the proposed estimators consistently outperform conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibit superior efficiency compared to existing ratio estimators that do incorporate auxiliary information.

Adaptive cluster sampling (ACS) is a sampling method commonly employed when the population is rare and exhibits clustering. However, the initial sample selection may include units that do not satisfy the specified condition. To address this, general inverse sampling is incorporated into ACS, where the initial units are selected sequentially and termination criteria are applied to regulate the number of rare elements drawn from the population. The objective of this study is to develop an estimator of the population mean by utilizing auxiliary information within the framework of general inverse adaptive cluster sampling. The proposed estimator, constructed on the basis of a regression-type estimator, is analytically examined. A simulation study was conducted to validate the theoretical results. In this study, the region of interest was divided into 400 square units (20 rows by 20 columns). The results demonstrate that the proposed estimator, which incorporates auxiliary variables, consistently yields a lower variance than the conventional mean estimator without auxiliary information. This superiority holds across all scenarios considered, specifically when the predetermined number of rare units r ranges from two to ten. Therefore, the proposed estimator is shown to be more efficient than the estimator that does not employ auxiliary information.