Empirical likelihood M‐estimation for the varying‐coefficient model with functional response
Bibliographic record
Abstract
Abstract This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels.
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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 | 0.099 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".