Measurement error in linear regression models with fat tails and skewed errors
Bibliographic record
Abstract
Linear regression models which account for skewed error distributions with fat tails have been previously studied. These two important features, skewness, and fat tails, are often observed in real data analyses. Covariates measured with an error also happen frequently in the observational data set-up. As a motivating example, wind speed as a covariate is usually used, among other covariates, to estimate the particulate matter (PM) which is one of the most critical air pollutants and has a major impact on human health and on the environment. However, the wind speed is measured with error and the distribution of PM is neither symmetric nor normally distributed (see Section “PM data application in Canada” for more details). Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to study properly linear regression models where the covariates are measured with error and the error distribution is skewed with fat tails. We use a hierarchical Bayesian approach for inference, addressing also sensitivity of the results to priors. Performance of the proposed approach is evaluated through a simulation study and also by a real data application (PM in Canada).
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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 | 0.052 | 0.181 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.005 | 0.005 |
| 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".