Digital economy has emerged as one of the primary driving forces for economic globalization. However, assessing digital economy development in a robust and scientific manner remains a great challenge. This paper proposes an evaluation system with measurement errors correction to accurately research the regional differences in and the spatial-temporal evolution characteristics of digital economy development in the Yangtze River Economic Belt (YEB), combining the entropy method, the Dagum–Gini coefficient, an $\sigma$ convergence model and grey correlation analysis. The results present that the digital economy development index in the YEB rose from 2012 to 2021, with the greatest weight being social livelihood benefits. Meanwhile, there were noticeable regional differences in digital economy development in the YEB; in particular, the middle reaches showed obvious convergence. The grey correlation degree between the influence factors and the digital economy development ranged from 0.5286 to 0.9144, demonstrating a robust positive correlation. The theoretical framework of this paper integrates economic development models with advanced statistical analysis techniques, providing a robust analytical perspective for examining the complexities of digital economy evolution. The insights offer a blueprint for policymakers seeking to foster a robust and equitable digital economy, underscoring the potential of data-driven policy formulations in navigating the intricate landscape of economic globalization.