Inadmissible estimators of normal quantiles and two-sample problems with additional information
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Bibliographic record
Abstract
<!-- *** Custom HTML *** --> We consider estimation problem of a normal quantile <i>μ</i>+<i>η</i><i>σ</i>. For the scale invariant squared error loss and unrestricted values of the population mean and standard deviation <i>μ</i> and <i>σ</i>, [13] established the inadmissibility of the MRE estimator for <i>η</i><i>≠</i>0. In this paper, we explore: (i) the impact of the loss with the study of scale invariant absolute value loss, and (ii) situations where there is a parameter space restriction of a lower bounded mean <i>μ</i>. We establish (i) the inadmissibility of the MRE estimator of <i>μ</i>+<i>η</i><i>σ</i>; <i>η</i><i>≠</i>0; under scale invariant absolute value loss; (ii) the inadmissibility of the Generalized Bayes estimator of <i>μ</i>+<i>η</i><i>σ</i>; <i>η</i><i>></i>0; under scale invariant squared error loss, associated with the prior measure 1<sub>(0,<i>∞</i>)</sub>(<i>μ</i>)1<sub>(0,<i>∞</i>)</sub>(<i>σ</i>) which represents the truncation of the usual non-informative prior measure onto the restricted parameter space. Both of these results are obtained through a conditional risk analysis and may be viewed as extensions of [13]. Finally, we provide further applications to two-sample problems under the presence of the additional information of ordered means.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.008 | 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