Transfer Learning for Linearized Maximum Rank Correlation Estimation

ABSTRACT Transfer learning has attracted considerable attention in various fields, as it effectively alleviates the problem of insufficient data in individual prediction tasks. In this paper, we propose a transfer learning method for linearized maximum rank correlation estimation under the single‐index model framework (denoted as T‐lmrc). The core idea of the proposed method is to improve the fitting accuracy and estimation reliability of the target data by screening and fusing informative auxiliary datasets. To address the problem that informative auxiliary sources are difficult to pre‐determine in practical applications, we specially design a transferable source detection process to accurately identify auxiliary sources that are helpful for the target task, eliminate invalid auxiliary sources, and avoid the interference of invalid information on the estimation results. On this basis, we further strictly prove the consistency of the proposed transferable source detection procedure under mild theoretical conditions, providing a solid theoretical guarantee for the effectiveness of the method. Extensive numerical experiments demonstrate that, regardless of whether the target model is correctly specified, the proposed T‐lmrc method outperforms the conventional linearized maximum rank correlation estimator using only target data (S‐lmrc), the method that directly merges target and auxiliary source data without screening (A‐lmrc), and the AIC weighting‐based method (Aic‐lmrc). The practical application value of the proposed method is further verified by its application to housing rental data in Shanghai and Beijing, respectively.