On pointwise laws of iterated logarithm for estimators of certain conditional functionals
Bibliographic record
Abstract
We study the estimation of certain functionals of the conditional distribution function with two classes of nonparametric estimators—the rank nearest neighbour (RNN) type estimators and the Nadaraya-Watson (NW) kernel type estimators. We obtain sharp pointwise rates of strong consistency by establishing laws of the iterated logarithm for these two classes of estimators. The results parallel those of Hall [Hall, P., 1981, Laws of the iterated logarithm for nonparametric density estimators. Zeitschrift Fur Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 56, 47–61] and Härdle [Härdle, W., 1984, A law of the iterated logarithm for nonparametric regression function estimators. The Annals of Statistics, 12, 624–635] for certain density and regression function estimators respectively, and extend those of Mehra et al. [Mehra, K.L., Rama Krishnaiah, Y.S. and Rao, S.M., 1992a, Asymptotic properties of smoothed vs. unsmoothed conditional distribution function estimators, Bulletin of Informatics and Cybernetics, 25, 71–97] on the strong consistency of smooth conditional distribution function estimators.
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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 | 0.072 | 0.357 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.012 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.005 | 0.007 |
| Research integrity | 0.004 | 0.009 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".