Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation
Bibliographic record
Abstract
The empirical multilinear or checkerboard copula process is a promising tool for statistical inference in copula models for data with ties (Genest et al., 2019a). The large-sample behavior of this process was determined in Genest et al. (2014, 2017) under very broad conditions. The purpose of this note is to provide a detailed description of this asymptotic result and to derive an expression for the limit of the process in the simplest possible case in which the data form a random sample of pairs of Bernoulli random variables. Although one would never actually fit a copula model to a 2 × 2 contingency table, this case is particularly well suited for explicit calculations and didactic explanations of the intricacies of the limiting behavior of this process and make it clear why the conditions in Genest et al. (2014, 2017) are needed and cannot be simplified.
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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 | 0.083 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".