HIGHER ORDER ASYMPTOTICS: AN INTRINSIC DIFFERENCE BETWEEN UNIVARIATE AND MULTIVARIATE MODELS
Bibliographic record
Abstract
summary Higher order asymptotic theory is targeted on the development of an asymptotic expansion for the distribution function of a statistic of interest. The asymptotic inference procedures are commonly based on simple characteristics of the density function at or near a data point of interest. In particular, exponential models are useful to provide accurate approximations to general statistical models. Typically, to the third order the exponential approximation has three primary parameters, two corresponding to pure model type and one for the departure from an exponential model (termed a non-exponentiality term). Andrews, Fraser and Wong (2005) discovered that to the third order, the observed significance function does not depend on the non-exponential term for univariate models. This finding has remarkable statistical implications for inference concerning univariate models. However, it is not clear whether this property holds for multivariate models. In this paper we address this question, and explore the intrinsic discrepancy between univariate and multivariate models.
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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 | 0.022 | 0.099 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 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".