Non‐parametric Estimator for Conditional Mode with Parametric Features*
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We in this paper propose a new approach for estimating conditional mode non‐parametrically to capture the ‘most likely’ effect built on local linear approximation, in which a parametric pilot modal regression is locally adjusted through a kernel smoothing fit to potentially reduce the bias asymptotically without affecting the variance of the estimator. Specifically, we first estimate a parametric modal regression utilizing prior information from initial studies or economic analysis, and then estimate the non‐parametric modal function based on the additive correction by eliminating the parametric feature. We derive the asymptotic normal distribution of the proposed modal estimator for both fixed and estimated parametric feature cases, and demonstrate that there is substantial room for bias reduction under certain regularity conditions. We numerically estimate the suggested modal regression model with the use of a modified modal‐expectation‐maximization (MEM) algorithm. Monte Carlo simulations and one empirical analysis are presented to illustrate the finite sample performance of the developed modal estimator. Several extensions, including multiplicative correction, generalized guidance, modal‐based robust regression and the incorporation of categorical covariates, are also discussed for the sake of completeness.
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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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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