Some Improvements of the Bootstrap over the Delta Method Probability Errors for Whittle Estimators
Bibliographic record
Abstract
The purpose of this paper is to compare the coverage probability errors of the parametric bootstrap with that of the delta method for the covariance parameters of a regression model with auto-regressive fractionally integrated moving average (ARFIMA) errors. We consider the coverage probability errors of both confidence intervals (CIs) and tests based on the the plug-in Whittle maximum likelihood (PWML) estimators. We first show that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of the two-sided delta method and parametric bootstrap confidence intervals on the plug-in Whittle likelihood estimator or the covariance parameter are shown to be $O(n^{-1})$ and $o(n^{-3/2}\ln{n})$, respectively, where n is the sample size. Next, we show that those of the one-sided parametric bootstrap confidence intervals are shown to be $O(n^{-1/2})$ and $o(n^{-1}\ln{n})$, respectively. These results show that for both one-sided and two-sided confidence intervals and tests, the bootstrap provides a significant improvement over that of the delta method.
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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 | 0.044 | 0.209 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| 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".