The t-Distribution in Financial Mathematics and Multivariate Testing Contexts
Bibliographic record
Abstract
The Student’s t-distribution provides a thematic connection between the historical and technical elements of this paper. The historical section offers a brief account of the early contributions of Chris Heyde and his collaborations with Madan and Seneta in the development of financial mathematics. The technical section focuses on hypothesis testing, motivated by the observation that, in a setting with pairwise exchangeable dependence for test statistics, the cutoff methods proposed by Sarkar and colleagues in 2016 can be viewed as a first iteration of the classical approach developed by Holm in 1979. These methods had already been refined earlier by Seneta and Chen in their work from 1997 and 2005, which laid the foundation for further improvements. Building on this, a new iteration of the Seneta-Chen method is presented, offering enhancements over the Sarkar approach. Numerical and graphical comparisons are provided, focusing on equal tails testing within the multivariate t-distribution framework. While the tabulated results clearly show improvements with the new procedure, the simulated family-wise error rates across varying correlations reveal only minor practical differences between the iterative methods. This suggests that, under suitable conditions, a single iteration suffices in practice. The paper concludes with personal reflections from the first author, sharing memories of Joe Gani and Chris Heyde, in keeping with the commemorative nature of this issue.
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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 | 0.016 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.002 | 0.018 |
| Scholarly communication | 0.007 | 0.011 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".