AN ASYMPTOTIC EXPANSION OF THE DISTRIBUTION OF THE DM TEST STATISTIC
Bibliographic record
Abstract
Asymptotically, the Distance Metric (DM) test statistic has a chi-squared distribu-tion. In practice, however, this is infeasible since the sample size is finite. It is expected that after Edgeworth expansion, the distribution of the corrected DM test statistic be closer to a chi-squared distribution than the uncorrected one. This paper mainly has three parts: in the theoretical part, Edgeworth approximation of the distribution of the DM test statistic is derived and a Bartlett-type correction factor is obtained; in the simulation part, examples of covariance structures are given to illustrate the theoretical results; in the application part, the theoretical results are applied to study the covari-ance structures of earnings. The contributions of this paper are: (i) it can be viewed as complementary to both Phillips and Park (1988) and Hansen (2006) in that it relaxes the basic requirement of nonlinear restrictions in some sense; (ii) it extends Hansen (2006) to multiple restrictions (possibly large number of degrees of freedom) and vari-ous models; (iii) it explains and provides a solution to the long-existing “troublesome” discrepancy puzzle in labor economics literature that a longer panel reverses the original inference; (iv) the theoretical results are distribution-free. JEL Classification: C12
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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 | 0.011 | 0.101 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 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".