Post-shrinkage strategies for nonlinear semiparametric regression models in low and high-dimensional settings
Bibliographic record
Abstract
This paper considers semiparametric estimation strategies for the nonlinear semiparametric regression model (NSRM) under the sparsity assumption by modifying the Gauss-Newton method for both low- and high-dimensional data scenarios. In the low-dimensional case, coefficients are partitioned into two parts that represent nonzero (strong signals) and sparse coefficients. In the high-dimensional case, a weighted-ridge approach is employed, and coefficients are partitioned into three parts, adding weak signals as well. Shrinkage estimators are then obtained in both cases. More importantly, in this paper, we assume that a nonlinear structure is present in the parametric component of the model, which makes the direct application of penalized least squares to the NSRM impossible. To solve this problem, we employ the iterative Gauss-Newton method to obtain the final NSRM estimators. We provide both theoretical and practical details for the suggested estimators. Asymptotic results are derived for both low- and high-dimensional cases. We conduct an extensive simulation study to evaluate the performance of the estimators in a practical setting. Moreover, we substantiate our findings with data examples from two distinct breast cancer datasets: the Breast Cancer in the United States (BCUS) and Wisconsin datasets. By demonstrating the effectiveness of our introduced estimators in these particular biostatistical contexts, our numerical study provides support for the theoretical efficacy of shrinkage estimators, suggesting their potential relevance to breast cancer research and biostatistical methodologies.
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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 | 0.010 | 0.025 |
| 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 | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".