Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators
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Bibliographic record
Abstract
Abstract For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.
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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) | 0.001 | 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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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