arXiv 10 Jul 2026 · Mathematics — Statistics Theory
arXiv:2607.09536 · PDF · DOI · OpenAlex · Extracted main text
For analytic convenience, existing statistical frameworks either assume random or fixed regressors. However, it is a little awkward that they do not cover the practical case of estimating the average treatment effect in experiments with randomized treatments and non-randomized, fixed pretreatment covariates. We unify the literature by providing the theory for regressions with mixed regressors that contain both random and fixed components. Importantly, our theory allows for misspecification of the regression functions. We first establish general results for estimating equations with both random and fixed components and then use it to analyze misspecified linear regression, with applications to completely randomized experiments. We focus on the causal interpretation of the regression coefficients and standard errors even when the models are wrong. We start with the theory for independent data and then extend the discussion to clustered data.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abadie, Alberto and Imbens, Guido W. and Zheng, Fanyin Inference for Misspecified Models With Fixed Regressors | 1.000 | 7 | 5 | 100% |
| 2 | White, Halbert Maximum Likelihood Estimation of Misspecified Models | 1.000 | 5 | 4 | 100% |
| 3 | Negi, Akanksha and Wooldridge, Jeffrey M Revisiting Regression Adjustment in Experiments with Heterogeneous Treatment Effects | 0.941 | 6 | 3 | 83% |
| 4 | Huber, Peter J The Behavior of Maximum Likelihood Estimates under Nonstandard Conditions | 0.928 | 4 | 3 | 100% |
| 5 | White, Halbert Using Least Squares to Approximate Unknown Regression Functions | 0.928 | 4 | 3 | 100% |
| 6 | Lin, Winston Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining Freedman's Critique | 0.874 | 5 | 2 | 100% |
| 7 | Liang, KUNG-YEE and Zeger, SCOTT L Longitudinal Data Analysis Using Generalized Linear Models | 0.811 | 4 | 2 | 100% |
| 8 | Su, Fangzhou and Ding, Peng Model-Assisted Analyses of Cluster-Randomized Experiments self | 0.794 | 10 | 3 | 50% |
| 9 | Imbens, Guido W. and Angrist, Joshua D Identification and Estimation of Local Average Treatment Effects | 0.737 | 4 | 3 | 50% |
| 10 | Abadie, Alberto and Athey, Susan and Imbens, Guido W and Wooldridge,… When Should You Adjust Standard Errors for Clustering?* | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 44 scored citations.