Non-asymptotic analysis on regression-based inference

Music City Center 

Regression-based inference is widely employed to analyze experimental data. We propose a non-asymptotic approach for estimating causal effects under homogeneous and heterogeneous linear models, utilizing Rao's score test within the maximum likelihood framework. Specifically, we address two heterogeneous settings: one assumes constant variance, while the other allows variance to depend on covariates. Unlike traditional asymptotic methods, which require large sample sizes with fixed parameter dimensions, our method derives explicit bounds that depend on covariate dimensions and variance assumptions, offering scalability and adaptability to diverse model settings. Under bounded variance and sub-Gaussian assumptions, we extend this framework to a quasi-likelihood setting for causal inference, applying it to hypothesis testing with Rao's score test and providing a robust tool for causal analysis and hypothesis testing across various applications.

Regression-based inference

non-asymptotic analysis

likelihood framework

quasi-likelihood framework 

Section on Statistical Learning and Data Science