Asymptotic theory and wild bootstrap inference with clustered errors
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Bibliographic record
Abstract
We study asymptotic inference based on cluster-robust variance estimators for regression models with clustered errors, focusing on the wild cluster bootstrap and the ordinary wild bootstrap. We state conditions under which both asymptotic and bootstrap tests and confidence intervals will be asymptotically valid. These conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity. To include power in the analysis, we allow the data to be generated under sequences of local alternatives. Under a somewhat stronger set of conditions, we also derive formal Edgeworth expansions for the asymptotic and bootstrap test statistics. Simulation experiments illustrate the theoretical results, and the Edgeworth expansions explain the overrejection of the asymptotic test and shed light on the choice of auxiliary distribution for the wild bootstrap.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it