Bibliographic record
Abstract
Many important statistics are functions of sample moments, for instance, sample skewness, sample kurtosis, sample odds ratio, sample correlation coefficient, sample quantiles, sample process capability indices [Kotz, S. and Johnson, N. L. (1993). Process Capability Indices. Chapman and Hall; Kotz, S. and Lovelace, C. R. (1998). Process Capability Indices in Theory and Practice. Arnold.], student t-type statistics, etc. In this article, we first derive the laws of the iterated logarithm for sample moments and then the laws of the iterated logarithm for sample skewness, sample kurtosis, sample odds ratio, and sample correlation coefficient. The other functions of sample moments can be dealt with without difficulty. The results provide the basis for concepts of 100% confidence intervals and tests of power 1 in statistical inferences [Robbins, H. (1970). Statistical methods related to the law of the iterated logarithm. Ann. Math. Stat., 41, 1397–1409; Robbins, H. and Siegmund, D. (1973). Statistical tests of power one and the integral representation of solutions of certain partial differential equations. Bull. Inst. Math. Acad. Sinica, 1, 93–120; Robbins, H. and Siegmund, D. (1974). The expected sample size of some test of power one. Ann. Stat., 2, 415–436; Lai, T. L. (1977). Power one tests based on sample sums. Ann. Stat., 5, 866–880.].
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".