Inference for Linear Models with Dependent Errors
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Bibliographic record
Abstract
Summary The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M-estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M-estimators. Methodologically, we extend the recently proposed self-normalized approach of Shao from stationary time series to the regression set-up, where the sequence of response variables is typically non-stationary in mean. Since the limiting distribution of the self-normalized statistic depends on the design matrix and its corresponding critical values are case dependent, we develop a simulation-based approach to approximate the critical values consistently. Through a simulation study, we demonstrate favourable finite sample performance of our method in comparison with a block-bootstrap-based approach. Empirical illustrations using two real data sets are also provided.
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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 | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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