Powerful Nonparametric Asymptotic Tests for Change in the Mean with Reduced Type I Errors
Bibliographic record
Abstract
We study numerically finite-sample power functions of nonparametric asymptotic tests for at most one change in the mean that are based on convergence in the distribution of sup- and integral functionals of an appropriately weighted and normalized tied-down partial sums process. For each test, a three-way trade-off is observed among its type I errors, power for detecting the change near the beginning or end of the sample, and power for detecting the change in the middle of the sample. By choosing suitable weight functions of a special form, we propose new sup- and integral tests that are shown to be nearly as powerful as the overall most powerful sup-test in the literature, regardless of where the change occurs in the sample. Moreover, the type I errors of the new tests are closer to the asymptotic significance level across various distributions and are lower and converge faster for distributions that are more asymmetric, heavy-tailed, or both.
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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 | 0.057 | 0.373 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".