Kernel Ridge-Type Shrinkage Estimators in Partially Linear Regression Models with Correlated Errors
Bibliographic record
Abstract
Partially linear time series models often suffer from multicollinearity among regressors and autocorrelated errors, both of which can inflate estimation risk. This study introduces a generalized ridge-type kernel (GRTK) framework that combines kernel smoothing with ridge shrinkage and augments it through ordinary and positive-part Stein adjustments. Closed-form expressions and large-sample properties are established, and data-driven criteria—including GCV, AICc, BIC, and RECP—are used to tune the bandwidth and shrinkage penalties. Monte-Carlo simulations indicate that the proposed procedures usually reduce risk relative to existing semiparametric alternatives, particularly when the predictors are strongly correlated and the error process is dependent. An empirical study of US airline-delay data further demonstrates that GRTK produces a stable, interpretable fit, captures a nonlinear air-time effect overlooked by conventional approaches, and leaves only a modest residual autocorrelation. By tackling multicollinearity and autocorrelation within a single, flexible estimator, the GRTK family offers practitioners a practical avenue for more reliable inference in partially linear time series settings.
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How this classification was reachedexpand
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".