Minimax robust designs for wavelet estimation of nonparametric regression models with autocorrelated errors
Bibliographic record
Abstract
We discuss the construction of designs for estimation of nonparametric regression models with autocorrelated errors when the mean response is to be approximated by a finite order linear combination of dilated and translated versions of the Daubechies wavelet bases with four vanishing moments. We assume that the parameters of the resulting model will be estimated by weighted least squares (WLS) or by generalized least squares (GLS). The bias induced by the unused components of the wavelet bases, in the linear approximation, then inflates the natural variation of the WLS and GLS estimates. We therefore construct our designs by minimizing the maximum value of the average mean squared error (AMSE). Such designs are said to be robust in the minimax sense. Our illustrative examples are constructed by using the simulated annealing algorithm to select an optimal [Formula: see text]-point design, which are integers, from a grid of possible values of the explanatory or design variable [Formula: see text]. We found that the integer-valued designs we constructed based on GLS estimation, have smaller minimum loss when compared to the designs for WLS or ordinary least squares (OLS) estimation, except when the correlation parameter [Formula: see text] approaches 1.
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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 | 0.018 | 0.032 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".