## 1 Introduction
Analyzing the impact of robotic automation and artificial intelligence-based solutions on bank performance is a topic of growing interest in the literature, but existing studies have not systematically explored how these technologies influence the profitability of financial institutions in relation to their performance level. While much of the research has focused on the general effects of automation on the banking sector, it has often neglected variations in these effects across different institutions' performance. In particular, the influence of automation on profitability may differ significantly between high performing banks and those with lower operational efficiency or financial performance, an issue that has not yet been sufficiently addressed in the literature. The main contribution of this study lies in applying the MMQR approach to capture the heterogeneity of the impact of automation and digitalization on return on equity (ROE) in the EU banking sector. MMQR is the best approach to capture the heterogeneity of the banking sector because it allows for modeling economic relationships at different levels of distribution, thus capturing specific effects across distribution quantiles, not just the average [51]. In the banking sector, large and small banks may react differently to economic changes, and MMQR can differentiate their impact, providing a more detailed analysis of the diversity in financial performance and associated risks [50]. This method is also useful for analyzing bank behavior in times of economic or regulatory crisis, where banks in different segments may experience significantly different effects on financial stability [45]. The novelty of the study lies in the simultaneous integration of physical automation, measured by the number of ATMs, and AI-driven solutions, reflected by the DESI-Integration of Digital Technology (IDT), DESI-Human Capital (HC) and the proportion of internet banking users, together with R&D investments. Unlike previous approaches, this analysis allows not only an estimation of the technological effects on banking performance, but also a deeper understanding of the mechanisms through which digitalization shapes the financial sector according to the level of competitiveness of each institution. In terms of implications for policymakers and regulators, the results provide relevant insights into the need to adapt regulatory and technology investment strategies to the heterogeneous realities of the banking sector. The identification of the asymmetric effects of automation and AI on the profitability of financial institutions suggests that standardized policies are not sufficient to ensure a smooth digital transition across EU member states. Thus, the implementation of customized measures to support the adoption of new technologies according to the specificities of each national banking system becomes imperative. In addition, stimulating investment in research and development in the field of financial technologies is essential to increase competitiveness and reduce the digital divide between member states. As regards the research gap in the literature, most of the available studies have focused either on the general impact of digitalization on the financial industry or on the effects of automation on employment, without investigating in depth how these transformations influence the distribution of banking performance. Also, existing empirical approaches have not used advanced regression methodologies to analyze the heterogeneity of technological effects on different segments of the financial market. This study advances existing research by applying the MMQR method to investigate the heterogeneous effects of automation and digitalization on bank performance, simultaneously integrating mechatronic technologies and artificial intelligence-based solutions and providing a detailed analysis of the diversity of their impact on the profitability of financial institutions.