发表机构
Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对协变量偏移场景，提出结合截断重要性加权核岭回归与乘数自助法的非参数拟合优度检验方法，经理论证明与数值实验验证其有效性。
AI 中文摘要
本文针对协变量偏移场景提出了非参数拟合优度检验方法，其中带标签数据来自源总体，而拟合优度针对目标总体进行评估。分布失配通过目标-源密度比的有界矩条件或次指数尾条件进行量化。我们的方法结合了截断重要性加权核岭回归与乘数自助法，以构建回归函数的置信集。该截断操作可稳定重要性加权核岭回归及自助校准过程，使得我们的方法在密度比具有重尾时仍适用。我们在合适的算子相容性条件下证明了所得置信集的非渐近有效性与尖锐性，并针对目标-源密度比及核积分算子的谱衰减的特定条件，建立了覆盖概率的显式误差率。数值实验验证了我们的理论结果。
英文摘要
This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target population. The distribution mismatch is quantified by either a bounded moment condition or a sub-exponential tail condition on the target-to-source density ratio. Our method combines truncated importance-weighting kernel ridge regression with a multiplier bootstrap to construct confidence sets for the regression function. The truncation stabilizes the importance- weighting kernel ridge regression as well as the bootstrap calibration, making our approach applicable even when the density ratio has heavy tails. We prove nonasymptotic validity and sharpness of the resulting confidence sets under suitable operator compatibility conditions, and establish explicit error rates for coverage probability under specific conditions on the target- to-source density ratio and on the spectral decay of the kernel integral operator. Numerical experiments corroborate our theoretical findings.
