Asymptotic Confidence Intervals for the Mean with Increased Finite-Sample Coverage Probabilities
Bibliographic record
Abstract
We consider a Student process based on independent copies of a random variable X. If X is in the domain of attraction of the normal law (DAN), a weighted version of the Student process is known to follow a functional Central Limit Theorem (FCLT). Accordingly, appropriate functionals of such a process converge in distribution to the same functionals of the similarly weighted standard Wiener process. We use such a convergence for an integral functional and derive asymptotic confidence intervals (CIs) for the mean of X. For right-skewed distributions of X in DAN, we show that the obtained CIs have higher finite-sample coverage probabilities than, and may be preferred over, a CI I1 of the same asymptotic confidence level 1−α that is based on the CLT for the Student t-statistic, since the finite-sample coverage probabilities of the latter CI may be lower than 1−α. Moreover, for such distributions, the finite-sample coverage probabilities of our best two CIs are also higher than those of their respective equal-expected-length I1 counterparts.
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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 | 0.004 | 0.024 |
| 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 | 0.001 | 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".