A bivariate density estimation method based on level crossings
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Bibliographic record
Abstract
Abstract This article introduces a method of nonparametric bivariate density estimation based on a bivariate sample level crossing function, which leads to the construction of a bivariate level crossing empirical distribution function (BLCEDF). An efficiency function for this BLCEDF relative to the classical empirical distribution function (EDF), is derived. The BLCEDF gives more efficient estimates than the EDF in the tails of any underlying continuous distribution, for both small and large sample sizes. On the basis of BLCEDF we define a bivariate level crossing kernel density estimator (BLCKDE) and study its properties. We apply the BLCEDF and BLCKDE for various distributions and provide results of simulations that confirm the theoretical properties. A real-world example is given. Keywords: efficiencybivariate sample level crossing functionnonparametric functional estimationbivariate order statistics AMS Subject Classification : Primary: 62G30Secondary: 62G05 Acknowledgements The authors are supported by NSERC Canada grants. The authors are grateful to the referees and the editor for very helpful comments on an earlier version of the paper. The comments helped us to improve the paper.
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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 | 0.000 | 0.003 |
| 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