M-estimation for varying coefficient models with a functional response in a reproducing kernel Hilbert space
Bibliographic record
Abstract
Modern neuroimaging research calls for statistical methods that can model dynamic relationships between a functional response and a set of covariates. Current methods, however, remain disparate and limited in their ability to robustly accommodate real-world data and integrate smoothness penalties. In this work, we propose an M-estimation framework for the varying-coefficient model with a functional response that encompasses both mean and quantile regression. To accommodate smoothness regularization and circumvent the stringent conditions on Fourier coefficients or the covariance operator’s eigenvalues imposed by traditional fixed-basis representations, we assume that the functional coefficient resides in a reproducing kernel Hilbert space. We show that our proposed estimator is minimax rate optimal and establish convergence properties of our modified alternating direction method of multipliers algorithm. We further propose combining a weighted M-estimator and a copula model to quantify within-subject spatial dependence to improve estimation accuracy. Simulation studies and a real-world analysis demonstrate the robustness of our proposed methods to outliers.
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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 | 0.009 | 0.026 |
| 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 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".