Kernel Ridge-Type Shrinkage Estimators in Partially Linear Regression Models with Correlated Errors
Bibliographic record
Abstract
This paper introduces ridge‐type kernel smoothing estimators for par-tially linear time‐series models that employ shrinkage estimation to han-dle autoregressive errors and severe multicollinearity in the parametric component. By combining a generalized ridge penalty with kernel smoothing, the proposed estimators solve inflated variances arising from linear dependencies among predictors, while also accounting for auto-correlation. Four well-known selection criteria—Generalized Cross Val-idation (GCV), Improved Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC), and Risk Estimation via Classical Pilots (RECP)—are used to optimally choose both the bandwidth and shrinkage parameters. We provide closed‐form expressions for these estimators, establish their asymptotic properties, and present a risk‐based analysis that highlights the benefits of ordinary and positive‐part shrinkage ex-tensions. Simulation studies confirm that the introduced shrinkage ap-proaches outperforms standard methods when predictors are strongly correlated, with this advantage growing as sample sizes increase. An ap-plication to airline delay time‐series data further illustrates the efficacy and practical interpretability of the introduced methodology.
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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 | 0.029 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".