发表机构
KU Leuven; Joint Research Center, European Commission（荷语鲁汶大学; 欧盟委员会联合研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对欧盟福祉数据的高维、缺失和异常问题，提出稳健多块PCA方法bloccPCA，同时处理案例、块和单元级异常，提供全局与块成分及诊断工具，经模拟和实证验证有效。
AI 中文摘要
国内生产总值（GDP）被广泛用于指导经济和社会决策，但它仅提供了福祉的部分视角。为此，欧盟（EU）已启动倡议，监测超越GDP的可持续与包容性福祉，开发涵盖健康、教育、环境和社会包容等维度的指标框架。这些指标自然按主题领域分组，政策制定者关注这些领域如何对全球福祉做出贡献，以及哪些指标解释了国家间的差异。然而，此类数据具有高维性，包含缺失值，并可能含有影响整个观测、特定主题领域或单个指标的异常值。我们引入了块级异常值，并提出了bloccPCA，一种稳健的多块主成分分析方法，可同时处理案例级、块级和单元级异常值以及缺失值。该方法提供稳健的全局成分以总结福祉的整体结构，同时通过稳健的块成分保留主题领域的贡献。它还提供了诊断工具，以识别异常是出现在案例、块还是单元层面。蒙特卡洛模拟和对欧盟福祉数据集的应用表明，bloccPCA为可持续与包容性福祉提供了有价值的见解。
英文摘要
Gross Domestic Product (GDP) is widely used to guide economic and social decision-making, but it provides only a partial view of wellbeing. For this reason, the European Union (EU) has launched initiatives to monitor sustainable and inclusive wellbeing beyond GDP, developing indicator frameworks that cover dimensions such as health, education, environment, and social inclusion. These indicators are naturally grouped into thematic areas, and policymakers are interested in understanding how these areas contribute to global wellbeing and which indicators explain differences across countries. However, such data are high-dimensional, contain missing values, and may include anomalies affecting entire observations, specific thematic areas, or individual indicators. We introduce blockwise outliers and propose bloccPCA, a robust multiblock PCA method that simultaneously handles casewise, blockwise, and cellwise outliers, as well as missing values. The method provides robust global components to summarize the overall structure of wellbeing, while preserving thematic-area contributions through robust blockcomponents. It also yields diagnostic tools to identify whether anomalies arise at the case, block, or cell level. Monte Carlo simulations and an application to the EU wellbeing dataset show that bloccPCA provides valuable insights into sustainable and inclusive wellbeing.
