Robust designs for wavelet approximations of regression models
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Bibliographic record
Abstract
We consider the construction of designs for the estimation of a regression function, when it is anticipated that this function is to be approximated by the dominant terms in its wavelet expansion. We consider both the Haar wavelet basis and the multiwavelet system. The experimenter estimates the coefficients of those wavelets included in the approximation, hoping that the omitted terms will be inconsequential. This introduces bias into the least squares estimates, which we propose handling at the design stage by one of two methods: (i) implementing a minimax robust design, which enjoys the property of minimizing the maximum value of an mse-based loss function, with the maximum being taken as the remainder in the wavelet expansion varies over an L2 -neighbourhood; (ii) implementing a minimum variance unbiased (mvu) design which, when employed with weighted least squares and weights derived here, minimizes the variance subject to a side condition of unbiasedness. For the Haar wavelet system we show that the uniform design is both minimax robust and mvu. For multiwavelet approximations we give examples of both minimax robust and mvu designs. Two examples from the nonparametric regression literature are discussed, and designs are presented for each type of wavelet approximation.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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