Asymptotically Optimal Regression Prediction Intervals and Prediction Regions for Multivariate Data
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Bibliographic record
Abstract
This paper presents asymptotically optimal prediction intervals and prediction regions. The prediction intervals are for a future response $Y_f$ given a $p \times 1$ vector $\bx_f$ of predictors when the regression model has the form $Y_i = m(\bx_i) + e_i$ where $m$ is a function of $\bx_i$ and the errors $e_i$ are iid from a continuous unimodal distribution. The prediction intervals have coverage near or higher than the nominal coverage for many techniques even for moderate sample size $n$, say $n >$ 10(model degrees of freedom). The prediction regions are for a future vector of measurements $\bx_f$ from a multivariate distribution. The nonparametric prediction region developed in this paper has correct asymptotic coverage if the data $\bx_1, ..., \bx_n$ are iid from a distribution with a nonsingular covariance matrix. For many distributions, this prediction region appears to have good coverage for $n > 20 p$, and this region is asymptotically optimal on a large class of elliptically contoured distributions. Hence the prediction intervals and regions perform well for moderate sample sizes as well as asymptotically.
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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 | 0.006 |
| 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