Asymptotic behavior of the empirical multilinear copula process under broad conditions
Bibliographic record
Abstract
The empirical checkerboard copula is a multilinear extension of the empirical copula, which plays a key role for inference in copula models. Weak convergence of the corresponding empirical process based on a random sample from the underlying multivariate distribution is established here under broad conditions which allow for arbitrary univariate margins. It is only required that the underlying checkerboard copula has continuous first-order partial derivatives on an open subset of the unit hypercube. This assumption is very weak and always satisfied when the margins are discrete. When the margins are continuous, one recovers the limit of the classical empirical copula process under conditions which are comparable to the weakest ones currently available in the literature. A multiplier bootstrap method is also proposed to replicate the limiting process and its validity is established. The empirical checkerboard copula is further shown to be a more precise estimator of the checkerboard copula than the empirical copula based on jittered data. Finally, the weak convergence of the empirical checkerboard copula process is shown to be sufficiently strong to derive the asymptotic behavior of a broad class of functionals that are directly relevant for the development of rigorous statistical methodology for copula models with arbitrary margins.
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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 | 0.007 | 0.060 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".