The Theil–Sen estimator in a measurement error perspective
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Bibliographic record
Abstract
<!-- *** Custom HTML *** --> In a simple measurement error regression model, the classical least squares estimator of the slope parameter consistently estimates a discounted slope, though sans normality, some other properties may not hold. It is shown that for a broader class of error distributions, the Theil–Sen estimator, albeit nonlinear, is a median-unbiased, consistent and robust estimator of the same discounted parameter. For a general class of nonlinear (including <i>R</i>–, <i>M</i>– and <i>L</i>– estimators), study of asymptotic properties is greatly facilitated by using some uniform asymptotic linearity results, which are, in turn, based on contiguity of probability measures. This contiguity is established in a measurement error model under broader distributional assumptions. Some asymptotic properties of the Theil–Sen estimator are studied under slightly different regularity conditions in a direct way bypassing the contiguity approach.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| 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