Maximum Bias Curves for Robust Regression with Non-elliptical Regressors
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Bibliographic record
Abstract
Maximum bias curves for some regression estimates were previously derived assuming that (i) the intercept term is known and/or (ii) the regressors have an elliptical distribution. We present a single method to obtain the maximum bias curves for a large class of regression estimates. Our results are derived under very mild conditions and, in particular, do not require the restrictive assumptions (i) and (ii) above. Using these results it is shown that the maximum bias curves heavily depend on the shape of the regressors' distribution which we call the x-configuration. Despite this big effect, the relative performance of different estimates remains unchanged under different x-configurations. We also explore the links between maxbias curves and bias bounds. Finally, we compare the robustness properties of some estimates for the intercept parameter.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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 | 0.000 |
| 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