Detecting heteroscedasticity in a simple regression model via quantile regression slopes
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.049 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".