AN ASYMPTOTIC EXPANSION OF THE DISTRIBUTION OF THE DM TEST STATISTIC
Why this work is in the frame
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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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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 | 0.000 |
| 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