Estimation of the Mean Vector of a Multivariate Elliptically Contoured Distribution
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Bibliographic record
Abstract
Abtsrcat This paper deals with the estimation of the mean vector θ of a p-variate elliptically contoured distribution, E p (θ,Σ, f) based on the sample Y 1 Y 2 ,..., Y N of size N of size N when it is suspected that for a p× r known matrix B, the hypothesis θ = Bη, η∈ R r may hold. We consider the following estimators, (i) the unrestricted estimator (UE), (ii) the restricted estimator (RE), (iii) the preliminary test estimator (PTE), (iv) the James—Stein estimator (JSE), and (v) the positive-rule Stein estimator (PRSE). The bias and the risk expressions under the squared loss function are obtained for the five estimators and compared. It is noted that the dominance properties of these estimators remain the same as under normal theory. Further, it is shown that the shrinkage factor of the Stein-type estimators is robust with respect to the mean and unknown mixing distributions.
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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 | 0.001 | 0.036 |
| 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 | 0.000 |
| 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 it