Varying-Coefficient Additive Models with Density Responses and Functional Auto-Regressive Error Process
Bibliographic record
Abstract
In many practical applications, data collected over time often exhibit autocorrelation, which, if unaccounted for, can lead to biased or misleading statistical inferences. To address this issue, we propose a varying-coefficient additive model for density-valued responses, incorporating a functional auto-regressive (FAR) error process to capture serial dependence. Our estimation procedure consists of three main steps, utilizing spline-based methods after mapping density functions into a linear space via the log-quantile density transformation. First, we obtain initial estimates of the bivariate varying-coefficient functions using a B-spline series approximation. Second, we estimate the error process from the residuals using spline smoothing techniques. Finally, we refine the estimates of the additive components by adjusting for the estimated error process. We establish theoretical properties of the proposed method, including convergence rates and asymptotic behavior. The effectiveness of our approach is further demonstrated through simulation studies and applications to real-world data.
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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 | 0.013 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.002 |
| 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".