A comparison of variance estimators with known and unknown population means
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Bibliographic record
Abstract
Variance is a concept that is key, yet often difficult to estimate in statistics. In this paper, we consider the problem of estimating the population variance when the population mean is known. We compare two estimators, one that incorporates the known population mean and another which estimates the population mean. The standard normal, standard exponential, and t distribution with 3 degrees of freedom are considered, with sample sizes of 5, 20, 50, and 100. It is determined that both estimators are unbiased. For the normal and exponential distributions, both estimators have similar variances; however, the estimator that incorporates the known mean has marginally lower variance, and thus is recommended. For the t(3) distribution, the variances of the estimators do not exist.
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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 | 0.000 |
| 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