Testing for No Effect in Functional Linear Regression Models, Some Computational Approaches
Why this work is in the frame
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Bibliographic record
Abstract
Abstract The functional linear regression model is a regression model where the link between the response (a scalar) and the predictor (a random function) is expressed as an inner product between a functional coefficient and the predictor. Our aim is to test at first for no effect of the model, i.e., the nullity of the functional coefficient. A fully automatic permutation test based on the cross covariance operator of the predictor and the response is proposed. The model can be, in an obvious way, extended to the case of several functional predictors. When testing for no effect of some covariate on the response the permutation test is no longer valid. An alternative pseudo-likelihood ratio test statistic is then introduced. The procedure can be applied in some way to test partial nullity of a functional coefficient. All procedures are illustrated and compared by means of simulation studies.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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