Delta Method Confidence Intervals for Linear Regression Processes With Long-memory Disturbances
Bibliographic record
Abstract
This paper provides third and fourth-order coverage probability errors of delta method confidence intervals (CIs) for the covariance parameters of a time series generated by a linear regression model with strongly dependent errors. The CIs are based on the plug-in maximum likelihood (PML) estimators. Bounds have been established on the coverage probability errors of one-and two-sided delta method CIs based on the plug-in log-likelihood (PLL) function under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values. It is shown that the the fourth order delta method CIs in the case of linear regression model with Gaussian, stationary and strongly dependent errors have coverage probability errors of O(n^-1) and that of the third-order has errors of O(n^-1/2) which is the same order of magnitude asymptotically as in the independent and identically distributed (iid) case.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".