Detecting heteroscedasticity in a simple regression model via quantile regression slopes
Why this work is in the frame
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Bibliographic record
Abstract
Consider the linear regression model Y=β X 1+α+τ (X)ϵ, where X and ϵ are independent random variables, ϵ has a mean of zero and variance σ2, and τ is some unknown function used to model heteroscedasticity. Many methods have been proposed for testing H 0: τ (X) ≡ 1, the hypothesis that the error term is homoscedastic, with most methods known to be unsatisfactory in terms of controlling the probability of a Type I error. This paper considers several approaches based on a quantile regression estimator, one of which (method N2) is recommended for general use. A minor goal is to report new results related to a method suggested by Koenker. Method N2 does not dominate Koenker’s method in terms of power, but as illustrated, the choice of method can make a considerable difference when testing H 0. In particular, situations occur where Koenker’s method is highly non-significant, yet method N2 rejects at the 0.01 level.
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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 | 0.002 |
| 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