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<p>Spatial autoregressive (SAR) models are widely used in economics, environmental science, and epidemiology to capture spatial spillovers, while transfer learning has become an essential tool for improving estimation with limited or high-dimensional data. Existing SAR transfer learning methods are typically developed under Gaussian-type modeling assumptions and do not explicitly incorporate transformation mechanisms. While such models perform well under symmetric response distributions, their flexibility may be limited when the response exhibits substantial skewness. We propose a novel Box–Cox SAR transfer learning framework that jointly estimates transformation and regression parameters and incorporates a bootstrap-based detection procedure to adaptively screen transferable sources. This framework unifies distributional adjustment, spatial dependence, and selective transfer within a single scheme. Simulation studies and an empirical analysis of California Housing data confirm its robustness and predictive improvements over conventional SAR and naive pooling, establishing a principled direction for applying transfer learning to complex and heterogeneous spatial systems.</p>

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Transfer learning for Box–Cox transformed spatial autoregressive models

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • Haixu Bian,
  • Yunquan Song

摘要

Spatial autoregressive (SAR) models are widely used in economics, environmental science, and epidemiology to capture spatial spillovers, while transfer learning has become an essential tool for improving estimation with limited or high-dimensional data. Existing SAR transfer learning methods are typically developed under Gaussian-type modeling assumptions and do not explicitly incorporate transformation mechanisms. While such models perform well under symmetric response distributions, their flexibility may be limited when the response exhibits substantial skewness. We propose a novel Box–Cox SAR transfer learning framework that jointly estimates transformation and regression parameters and incorporates a bootstrap-based detection procedure to adaptively screen transferable sources. This framework unifies distributional adjustment, spatial dependence, and selective transfer within a single scheme. Simulation studies and an empirical analysis of California Housing data confirm its robustness and predictive improvements over conventional SAR and naive pooling, establishing a principled direction for applying transfer learning to complex and heterogeneous spatial systems.