Estimation of the Mean Vector of a Multivariate Elliptically Contoured Distribution
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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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".