Selection Bias Adjustment by Functional Transfer Learning via Reproducing Kernel Hilbert Space

As accessibility to different data sources increases, transfer learning becomes prevalent in improving statistical efficiency by integrating different datasets. In this article, we focus on the popular non-probability sampling from a finite population and propose a functional transfer learning method to adjust its selection bias through calibrating marginal means of functions in a reproducing kernel Hilbert space by incorporating a reference probability sample. Compared with existing works, the proposed method is more robust since no parametric assumption is made for both regression and selection models. Besides, the proposed method is multitask-oriented in the sense that the estimated sample weights can be used to estimate different population parameters. Theoretical properties, including consistency and a limiting distribution, are established under some regularity conditions. Numerical experiments show that the proposed estimator outperforms its competitors. The proposed method is applied to the second round economic census data in China as an empirical illustration.