Adaptive Regression on the Real Line in Classes of Smooth Functions
Bibliographic record
Abstract
Abstract: Adaptive pointwise estimation of an unknown regression function f(x), x ∈ R corrupted by additive Gaussian noise is considered in the equidistant design setting. The function f is assumed to belong to the class A(α) of functions whose Fourier transform are rapidly decreasing in the weighted L2-sense. The rate of decrease is described by a weight function that depends on the vector of parameters α which, in the adaptive setting, is typically unknown. For any of the classes A(α), α fixed, we describe minimax estimators up to a constant as the bin-width goes to zero. Conditions under which an adaptive study is suitable are presented and a notion of adaptive asymptotic optimality is introduced based on distinguishing, among all possible functional scales, between the so-called non-parametric (NP) and pseudo-parametric (PP) scales. We propose adaptive estimators which ‘tune up ’ point-wisely to the unknown smoothness of f. We prove them to be asymptotically adaptively minimax for large collections of NP functional scales, subject to being rate efficient for any of the PP functional scales.
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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 | 0.008 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| 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".