Boundary performance of the beta kernel estimators
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Bibliographic record
Abstract
The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] further show that beta kernel estimators have better finite sample performance than some of the widely used boundary corrected estimators. However, our study finds that the numerical comparisons of Chen are confounded with the choice of the bandwidths and the quantities being compared. In this paper, we show that the performances of the beta kernel estimators are very similar to that of the reflection estimator, which does not have the boundary problem only for densities exhibiting a shoulder at the endpoints of the support. For densities not exhibiting a shoulder, we show that the beta kernel estimators have a serious boundary problem and their performances at the boundary are inferior to that of the well-known boundary kernel estimator.
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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 | 0.017 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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