Inject Machine Learning into Significance Test for Misspecified Linear Models

TL;DR

This paper introduces an assumption-free method that integrates machine learning with significance testing to improve linear approximation and significance assessment in both linear and non-linear models.

Contribution

The paper proposes a novel machine learning-based approach for significance testing that does not rely on linear assumptions, outperforming traditional linear regression in non-linear scenarios.

Findings

Outperforms linear regression in non-linear ground truth cases

Provides theoretical guarantees for the estimator's properties

Offers a more reliable significance test in complex models

Abstract

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.