STUDENTIZED PARTIAL SCORE TESTS FOR VARIANCES IN LONGITUDINAL DATA
Bibliographic record
Abstract
Koenker9studied a studentized version of Neyman's score statistic and obtained theoretical results which indicated that the studentized version will outperform the score test under a linear model if the data is from a heavy-tailed t-distribution. However, the author failed to examine the size and power performances of the studentized test through a simulation study. Subsequently, Cai, Hurvich and Tsai7after a simulation study in a nonparametric setting, found that even when the data is from a normal population the score test was biased in estimating a pre-assigned level of significance. Thus, he recommended that the studentized score test should be used in all situations. Several authors have, however, shown earlier that when the data is from a normal population, Neyman's partial score test is asymptotically unbiased in estimating a pre-assigned level of significance. As a result in this paper, we obtain the partial score statistic and the studentized version under various models but conduct our simulation studies under the special case considered by Cai et al.7in order to examine the studentized test. We found, in our simulation studies, that when the model of interest is nonparametric with uncorrelated errors, the power of the score test is generally higher than that of the studentized test. The difference in power performances becomes more pronounced under the heavy-tailed t-distribution. In the normal case, both the partial score test and its studentized version performed well in controlling the size of the test. We also found that if the score statistic is constructed based on the underlying distribution of the data, then the score statistic will always outperform the studentized test in both power and size.
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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 | 0.040 | 0.233 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".