A note on trigonometric regression in the presence of Berkson‐type measurement error
Bibliographic record
Abstract
In this note, we study how parameter vector estimation for a trigonometric regression model and the expected squared residual error computed from an estimated model are affected by Berkson‐type measurement error. Closed‐form expressions for the parameter vector and the expected squared residual error are obtained by assuming that the observed covariate data are sampled from an equispaced design and that measurement error is generated from a symmetric probability distribution with a mean of zero. Notably, these results indicate that estimates of the amplitude parameters for a trigonometric regression model suffer from attenuation bias when covariate data are mis‐measured, and that estimates of the phase‐shift parameters are unbiased.
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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 | 0.083 | 0.313 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".