Homogeneity testing under finite location-scale mixtures
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Bibliographic record
Abstract
The testing problem for the order of finite mixture models has a long history and remains an active research topic. Since Ghosh and Sen (1985) revealed the hard-to-manage asymptotic properties of the likelihood ratio test, there has been marked progress. The most successful attempts include the modified likelihood ratio test and the EM-test, which lead to neat solutions for finite mixtures of univariate normal distributions, finite mixtures of single-parameter distributions, and several mixture-like models. The problem remains challenging, and there is still no generic solution for location-scale mixtures. In this paper, we provide an EM-test solution for homogeneity for finite mixtures of location-scale family distributions. This EM-test has nonstandard limiting distributions, but we are able to find the critical values numerically. We use computer experiments to obtain appropriate values for the tuning parameters. A simulation study shows that the fine-tuned EM-test has close to nominal type I errors and very good power properties. Two application examples are included to demonstrate the performance of the EM-test.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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