Goodness-of-fit tests based on sup-functionals of weighted empirical processes
Bibliographic record
Abstract
A large class of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes is proposed and studied. The weight functions employed are Erdős-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian bridge. Based on the result of M. Csörgő, S. Csörgő, Horváth, and Mason obtained for this type of test statistics, we provide the asymptotic null distribution theory for the class of tests in hand, and present an algorithm for tabulating the limit distribution functions under the null hypothesis. A new family of nonparametric confidence bands is constructed for the true distribution function and it is found to perform very well. The results obtained, together with a new result on the convergence in distribution of the higher criticism statistic, introduced by Donoho and Jin, demonstrate the advantage of our approach over a common approach that utilizes a family of regularly varying weight functions. Furthermore, we show that, in various subtle problems of detecting sparse heterogeneous mixtures, the proposed test statistics achieve the detection boundary found by Ingster and, when distinguishing between the null and alternative hypotheses, perform optimally adaptively to unknown sparsity and size of the non-null effects.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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".