Existing facial age estimation studies have mostly focused on intra-database protocols that assume training and test images are captured under similar conditions. This is rarely valid in practical applications, where we typically encounter training and test sets with different characteristics. In this paper, we deal with such situations, namely subjective-exclusive cross-database age estimation. We formulate the age estimation problem as the distribution learning framework, where the age labels are encoded as a probability distribution. To improve the cross-database age estimation performance, we propose a new loss function which provides a more robust measure of the difference between ground-truth and predicted distributions. The desirable properties of the proposed loss function are theoretically analysed and compared with the state-of-the-art approaches. In addition, we compile a new balanced large-scale age estimation database. Last, we introduce a novel evaluation protocol, called subject-exclusive cross-database age estimation protocol, which provides meaningful information of a method in terms of the generalisation capability. The experimental results demonstrate that the proposed approach outperforms the state-of-the-art age estimation methods under both intra-database and subject-exclusive cross-database evaluation protocols. In addition, in this paper, we provide a comparative sensitivity analysis of various algorithms to identify trends and issues inherent to their performance.