Robust kernel estimator for densities of unknown smoothness
Bibliographic record
Abstract
Results on non-parametric kernel estimators of density differ according to the assumed degree of density smoothness. A kernel/bandwidth pair that was optimal for a twice differentiable function may not be suitable when the density is piecewise linear. If there is uncertainty about the degree of smoothness, an inappropriate choice may lead to under- or oversmoothing. To examine various possible outcomes we provide asymptotic results on kernel estimation of a continuous density for an arbitrary bandwidth/kernel pair and derive the limit joint distribution of kernel density estimators corresponding to different bandwidths and kernel functions. Using these results, we propose a combined estimator constructed as an optimal linear combination of several estimators with different bandwidth/kernel pairs. Its theoretical properties [Kotlyarova, Y. and Zinde-Walsh, V., 2006, Non- and semi-parametric estimation in models with unknown smoothness. Economics Letters, 93, 379–386] are such that it automatically attains the best possible rate without a priori knowledge of the degree of smoothness. Our Monte-Carlo results confirm the advantages of the combined estimator of density.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.059 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".