提出一种更优的回归误差估计方法，显著降低偏差与方差。
Generalized Resubstitution for Regression Error Estimation
- 用不同经验概率测度和损失函数构造泛化重抽样估计器。
- 实验显示在有限样本下偏差与方差均优于传统平方和方法。
- 适合需要精准误差评估的统计建模与机器学习研究者。
我们为回归问题提出一类广义重抽样误差估计器，其涵盖多种经验概率测度与损失函数的组合。标准平方和准则仅为其中一种特例，对应于标准经验测度与二次损失。其他经验测度选择可带来更具优势的偏差与方差性质。我们在广泛假设下证明了这些估计器的一致性。同时提出了基于矩法与最大伪似然的测度选择方法并进行验证。多项式回归的详细实验结果表明，所提估计器在有限样本下具有更优的偏差与方差表现。实验的R代码已提供。
原文摘要 · Abstract (English)
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case corresponding to the standard empirical probability measure and the quadratic loss. Other choices of empirical probability measure lead to more general estimators with superior bias and variance properties. We prove that these error estimators are consistent under broad assumptions. In addition, procedures for choosing the empirical measure based on the method of moments and maximum pseudo-likelihood are proposed and investigated. Detailed experimental results using polynomial regression demonstrate empirically the superior finite-sample bias and variance properties of the proposed estimators. The R code for the experiments is provided.
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