Modeling non-normality using multivariate<i>t</i>: implications for asset pricing
Bibliographic record
Abstract
Purpose The purpose of this paper is to show that multivariatet-distribution assumption provides a better description of stock return data than multivariate normality assumption. Design/methodology/approach The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference. Findings The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariatet-distribution assumption can often be adequate. Conclusions under normality vs undertcan be drastically different for estimating expected returns and Jensen’sαs, and for testing asset pricing models. Practical implications The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management. Originality/value The authors proposed new procedures that makes it easy to use a multivariatet-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.
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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 | 0.027 | 0.142 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| 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".