RAD-Median and trimmed mean, new multivariate generalizations of the classical estimators
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Many statistical concepts are defined in the one-dimensional setting. It is not always clear how to generalize these concepts to higher dimensions. There are many multivariate generalizations of the median which are equivalent to the well-known one-dimensional median in the case of univariate data. Multivariate medians found in the literature lack desirable properties, such as being hard to compute for high dimensional data, or not having rotational invariance. We propose new multivariate estimators, RAD-Median and Zt-Mean, as generalizations of the one-dimensional sample median and trimmed mean, respectively, noting that the median is a special case of the trimmed mean. The parameter t in Zt-Mean controls the trimming proportion. The new estimators are simple and easy to compute and have various desirable properties, such as shift invariance, rotational invariance, and robustness. Simulation results indicate that the RAD-Median has the smallest absolute bias for large sample size and small fraction of outliers, among several other estimators in the literature including L1 median and depth median. Zt-Mean has the smallest mean squared error for some value of t, which depends on the fraction of outliers in the data.
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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) | 0.000 | 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