Abstract: Domain adaptation addresses the challenge where the distribution of target inference data differs from that of the source training data. Recently, data privacy has become a significant constraint, limiting access to the source domain. To mitigate this issue, Source-Free Domain Adaptation (SFDA) methods bypass source domain data by generating source-like data or pseudo-labeling the unlabeled target domain. However, these approaches often lack theoretical grounding. In this work, we provide a theoretical analysis of the SFDA problem, focusing on the general empirical risk of the unlabeled target domain. Our analysis offers a comprehensive understanding of how representativeness, generalization, and variety contribute to controlling the upper bound of target domain empirical risk in SFDA settings. We further explore how to balance this trade-off from three perspectives: sample selection, semantic domain alignment, and a progressive learning framework. These insights inform the design of novel algorithms. Experimental results demonstrate that our proposed method achieves state-of-the-art performance on three benchmark datasets—Office-Home, DomainNet, and VisDA-C—yielding relative improvements of $3.2\%$, $9.1\%$, and $7.5\%$, respectively, over the representative SFDA method, SHOT.