Generalised local polynomial estimators of smooth functionals of a distribution function with nonnegative support
Bibliographic record
Abstract
This paper introduces generalised smooth asymmetric kernel estimators for smooth functionals with non-negative support. More precisely, for $ x\in [0, \infty ), $ x∈[0, ∞), and for a functional, $ \Phi (x, F) $ Φ(x, F) of the distribution function F, we develop estimators of the functional Φ and its derivatives. The proposed estimator can be seen as the solution to a minimisation problem in the polynomial space $ L^2(q), $ L2(q), where q is an asymmetric density function. The framework presented here covers several classical nonparametric functional estimators and is linked with estimation using hierarchical kernels. We establish the asymptotic properties of the proposed estimators in the general framework. Furthermore, special attention is paid to comparing the asymptotic mean integrated square error (AMISE) of the proposed estimator with that of other classical symmetric/asymmetric density estimators. Additionally, a comparison of finite sample behaviour is conducted for both density estimation and hazard rate estimation via simulation and real data application.
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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 | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".