将机器学习引入误定线性模型的显著性检验
Inject Machine Learning into Significance Test for Misspecified Linear Models
摘要：
由于线性回归具有很强的可解释性，在社会科学中得到了广泛的应用，在传统的统计推断中，显著性检验通过线性回归提供了模型或系数的显著性水平。然而，线性回归方法依赖于地面真值函数的线性假设，这在实践中不一定成立。因此，即使对于简单的非线性情况，线性回归也可能无法报告正确的显著性水平。在本文中，我们提出了一个简单而有效的线性和非线性情况下的线性逼近的无偏方法。首先，我们应用机器学习方法来拟合训练集上的地面真值函数并计算其线性近似。之后，我们通过添加基于验证集的调整来获得估计量。我们证明了我们的估计量的浓度不等式和渐近性质，从而导致相应的显著性检验。实验结果表明，我们的估计显着优于线性回归的非线性地面真值函数，表明我们的估计可能是一个更好的工具的显着性测试。
英文摘要：
Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear regression methods rely on the linear assumptions of the ground truth function, which do not necessarily hold in practice. As a result, even for simple non-linear cases, linear regression may fail to report the correct significance level. In this paper, we present a simple and effective assumption-free method for linear approximation in both linear and non-linear scenarios. First, we apply a machine learning method to fit the ground truth function on the training set and calculate its linear approximation. Afterward, we get the estimator by adding adjustments based on the validation set. We prove the concentration inequalities and asymptotic properties of our estimator, which leads to the corresponding significance test. Experimental results show that our estimator significantly outperforms linear regression for non-linear ground truth functions, indicating that our estimator might be a better tool for the significance test.
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