On the minimax robustness against correlation and heteroscedasticity of ordinary least squares among generalized least squares estimates of regression
Bibliographic record
Abstract
Summary We revisit a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable form of dependence is in fact independence, so that a procedure optimal for independent and identically distributed data can be minimax. In particular, the ordinary least squares estimate of a correctly specified regression response is minimax among generalized least squares estimates, when the maximum is taken over certain classes of error covariance structures and the loss function possesses a natural monotonicity property. In regression models whose response function is possibly misspecified, ordinary least squares is minimax if the design is uniform on its support, but this often fails otherwise. An investigation of the interplay between minimax generalized least squares procedures and minimax designs leads us to extend, to robustness against dependencies, an existing observation: that robustness against model misspecifications is increased by splitting replicates into clusters of observations at nearby locations.
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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 | 0.060 | 0.164 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".