A new adaptive local polynomial density estimation procedure on complicated domains
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Bibliographic record
Abstract
This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both simple domains, such as open connected sets, and more complicated domains that are not star-shaped around the point of estimation. This enables us to handle domains with sharp concavities, holes, and local pinches, such as polynomial sectors. Additionally, we introduce a data-driven selection rule based on the general ideas of Goldenshluger and Lepski. Our results demonstrate that the local polynomial estimators are minimax under a $L^2$ risk across a wide range of Hölder-type functional classes. In the adaptive case, we provide oracle inequalities and explicitly determine the convergence rate of our statistical procedure. Simulations on polynomial sectors show that our oracle estimates outperform those of the most popular alternative method, found in the sparr package for the R software. Our statistical procedure is implemented in an online R package which is readily accessible.
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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 | 0.001 |
| 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 | 0.001 |
| 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