A Family of Goodness‐of‐Fit Tests for Copulas Based on Characteristic Functions
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Bibliographic record
Abstract
Abstract A general class of rank statistics based on the characteristic function is introduced for testing goodness‐of‐fit hypotheses about the copula of a continuous random vector. These statistics are defined as L 2 weighted functional distances between a nonparametric estimator and a semi‐parametric estimator of the characteristic function associated with a copula. It is shown that these statistics behave asymptotically as degenerate V ‐statistics of order four and that the limit distributions have representations in terms of weighted sums of independent chi‐square variables. The consistency of the tests against general alternatives is established and an asymptotically valid parametric bootstrap is suggested for the computation of the critical values of the tests. The behaviour of the new tests in small and moderate sample sizes is investigated with the help of simulations and compared with a competing test based on the empirical copula. Finally, the methodology is illustrated on a five‐dimensional data set.
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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 | 0.000 | 0.005 |
| 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