Author
Listed:
- Ziyuan Wang
- Lei Wang
- Heng Lian
Abstract
Through exploiting information from the source data to improve the fit performance on the target data, transfer learning estimations for high‐dimensional linear regression models have drawn much attention recently, but few studies focus on statistical inference and robust learning in the presence of heavy‐tailed/asymmetric errors. Using adaptive Huber regression (AHR) to achieve the bias and robustness tradeoff, in this paper we propose a robust transfer learning algorithm with high‐dimensional covariates, then construct valid confidence intervals and hypothesis tests based on the debiased lasso approach. When the transferable sources are known, a two‐step ℓ1‐penalized transfer AHR estimator is firstly proposed and the error bounds are established. To correct the biases caused by the lasso penalty, a unified debiasing framework based on the decorrelated score equations is considered to establish asymptotic normality of the debiased lasso transfer AHR estimator. Confidence intervals and hypothesis tests for each component can be constructed. When the transferable sources are unknown, a data‐driven source detection algorithm is proposed with theoretical guarantee. Numerical studies verify the performance of our proposed estimator and confidence intervals, and an application to Genotype‐Tissue Expression data is also presented.
Suggested Citation
Ziyuan Wang & Lei Wang & Heng Lian, 2024.
"Double debiased transfer learning for adaptive Huber regression,"
Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1472-1505, December.
Handle:
RePEc:bla:scjsta:v:51:y:2024:i:4:p:1472-1505
DOI: 10.1111/sjos.12723
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