Bootstrapped Pivots for Means of Short and Long Memory Linear Processes
Bibliographic record
Abstract
Re-sampling only once, with replacement, from the entire set of observations (without dividing them into blocks) from short or long memory linear processes, we construct direct randomized parametric and nonparametric (Studentized) pivots for the population mean. In the included numerical studies, the resulting pivots will be seen to significantly outperform the traditional t-statistic as a pivot for the population mean. Our approach to the bootstrap in this exposition is fundamentally different from the classical methods of the bootstrap that have been used when the population mean is the parameter of interest. In the latter a relatively large number of independent bootstrap sub-samples are drawn from the original data to estimate the sampling distribution of the traditional t-statistic, when the latter itself is studied in reference to making inference about the population mean. Using the approach of this paper, one does not encounter the well-known issues with bootstrapped t-statistics for dependent data. Hence, no adjustments such as block-bootstrapping are required. This is so, since the re-sampling mechanism in our introduced pivots for the population mean preserves the covariance structure of the observables in hand.
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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 | 0.011 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".