Homogeneity testing under finite location‐scale mixtures
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 & Sen (1985) revealed the hard‐to‐manage asymptotic properties of the likelihood ratio test, many successful alternative approaches have been developed. 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 article, 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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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 | 0.032 | 0.187 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".