A Competitor of the Kolmogorov--Smirnov Test for the Goodness-of-fit Problem
Bibliographic record
Abstract
The classical goodness-of-fit problem, in the case of a null continuous and completely specified distribution, is faced by a new version of the Girone--Cifarelli test (see Girone, 1964; Cifarelli, 1974 \& 1975). This latter test was introduced for the two-sample problem and showed a substantial gain of power over other common tests based on the empirical distribution function, notably over the Kolmogorov--Smirnov test. First, the problem of the re-definition of the Girone--Cifarelli test-statistic is considered, by reviewing the literature on the subject. A classical remark by Anderson (1962) is shown to be useful to choose the integrating function in the newly defined test-statistic. The sample properties of such a test-statistic are then studied. A table of critical values is obtained by simulation; moreover, the asymptotic null distribution is considered and its accuracy as an approximation of the finite distribution is discussed. Finally, a simulation study, considering a wide set of distributions mostly used in applications, is conducted to compare the proposed test with its classical competitors. The study gives some indications to locate such situations where the Girone-Cifarelli test performs at its best, notably over the Kolmogorov--Smirnov 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 | 0.030 | 0.144 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".