Multivariate kernel regression in vector and product metric spaces
Bibliographic record
Abstract
Nonparametric kernel regression is widely used in econometrics and has been applied to models with cross-sectional, time series and panel data. As functional data analysis is gaining attention, our analysis extends to the presence of multiple functional regressors or a mixture of functional and scalar regressors. We addresspoint-wise asymptotic properties of the estimators by relaxing restrictive smoothness assumptions on the conditioning distribution. Firstly, we establish the rate and asymptotic normality for the Nadaraya-Watson estimator for arbitrary conditioning distributions in $R^{q};$ for an absolutely continuous distribution we provide statistical guarantees for the standard rate and the asymptotic normality without requiring further smoothness. We demonstrate faster convergence associated with dimension reducing types of singularity, such as a fractal structure or a factor structure in the regressors. Second, the paper extends the limit theory 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.
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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 | 0.011 | 0.047 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 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".