Cellwise, Blockwise, and Casewise Robust Multiblock PCA for Sustainable and Inclusive Wellbeing in the EU

2026-10-02

AI Summary

This study addresses the challenges of high dimensionality, missing data, and multi-level outlier interference in European Union well-being indicator datasets, overcoming the limitations of GDP-centric assessments. We propose blocPCA, a robust multi-block principal component analysis method that introduces the novel concept of "block anomalies." By integrating robust statistics with missing value imputation algorithms, blocPCA enables simultaneous detection of case-, block-, and cell-level anomalies alongside missing data handling. It generates stable global and thematic components while preserving thematic contributions and precisely diagnosing anomaly sources. Simulation and empirical analyses demonstrate that blocPCA effectively identifies multidimensional anomalies, providing critical insights and methodological support for evaluating sustainable and inclusive well-being across the European Union.

Abstract

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.

Problem

• Multiblock PCA
• Robust statistics
• Wellbeing indicators
• Outlier detection
• High-dimensional data

Innovation

• Robust Multiblock PCA
• Blockwise Outliers
• Cellwise Outliers
• Casewise Outliers
• Missing Values