Two Bootstrap Strategies for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-Problem up to Location-Scale with Dependent Samples
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Bibliographic record
Abstract
This paper extends the work of Quessy and Éthier (2012) who considered tests for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-sample problem with dependent samples. Here, the marginal distributions are allowed, under<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, to differ according to their mean and their variance; in other words, one focuses on the shape of the distributions. Although easily stated, this problem nevertheless requires a careful treatment for the computation of valid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:math>values. To this end, two bootstrap strategies based on the multiplier central limit theorem are proposed, both exploiting a representation of the test statistics in terms of a Hadamard differentiable functional. This accounts for the fact that one works with empirically standardized data instead of the original observations. Simulations reported show the nice sample properties of the method based on Cramér-von Mises and characteristic function type statistics. The newly introduced tests are illustrated on the marginal distributions of the eight-dimensional Oil currency data set.
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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 | 0.001 | 0.002 |
| 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 | 0.000 | 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 it