Nonparametric estimation of a maximum of quantiles
Bibliographic record
Abstract
A simulation model of a complex system is considered, for which the outcome is described by $m(p,X)$, where $p$ is a parameter of the system, $X$ is a random input of the system and $m$ is a real-valued function. The maximum (with respect to $p$) of the quantiles of $m(p,X)$ is estimated. The quantiles of $m(p,X)$ of a given level are estimated for various values of $p$ from an order statistic of values $m(p_{i},X_{i})$ where $X,X_{1},X_{2},\dots$ are independent and identically distributed and where $p_{i}$ is close to $p$, and the maximal quantile is estimated by the maximum of these quantile estimates. Under assumptions on the smoothness of the function describing the dependency of the values of the quantiles on the parameter $p$ the rate of convergence of this estimate is analyzed. The finite sample size behavior of the estimate is illustrated by simulated data and by applying it in a simulation model of a real mechanical system.
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How this classification was reachedexpand
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 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".