Advancements in shrinkage estimation utilizing robust parameters for the Birnbaum-Saunders distribution in the case of multiple samples
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Bibliographic record
Abstract
In this study, we expanded the improved estimation strategies for robust estimators of the Birnbaum-Saunders distribution for the shape parameter for multiple samples while integrating sample and uncertain prior information. We have used the following estimators: the Graybill-Deal type estimator, the linear shrinkage estimator, the pretest estimator, the shrinkage preliminary estimator, the James-stein and positive James-stein estimation techniques. We developed a test statistic to accept or reject the null hypothesis when considering uncertain prior information. We also explored the asymptotic properties of the proposed estimators. To evaluate their effectiveness, we conducted Monte Carlo simulations using various parameter values and sample sizes that align with our theoretical findings. Additionally, we included a real data example to illustrate the estimators performance in real life application. Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 65-79
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it