Multivariate kernel regression in vector and product metric spaces
Bibliographic record
Abstract
This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in R q . In functional regression limit properties are established for multivariate functional regression. The rate and asymptotic normality for the Nadaraya–Watson (NW) estimator is established for distributions of regressors in R q that allow for mass points, factor structure, multicollinearity and nonlinear dependence, as well as fractal distribution; when bounded density exists we provide statistical guarantees for the standard rate and the asymptotic normality without requiring smoothness. We demonstrate faster convergence associated with dimension reducing types of singularity, such as a fractal distribution or a factor structure in the regressors. The paper extends asymptotic normality of kernel functional regression to multivariate regression over a product of any number of metric spaces. Finite sample evidence confirms rate improvement due to singularity in regression over R q . For functional regression the simulations underline the importance of accounting for multiple functional regressors. We demonstrate the applicability and advantages of the NW estimator in our empirical study, which reexamines the job training program evaluation based on the LaLonde data.
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How this classification was reachedexpand
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 | 0.001 | 0.032 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".