Multivariate Location: Robust Estimators And Inference
Bibliographic record
Abstract
The sample mean can have poor efficiency relative to various alternative estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) estimators have been proposed for dealing with this problem, but a comparison of various estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the skipped estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal 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 | 0.014 | 0.073 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".