On Smoothed MWSD Estimation of Mixing Proportion
Bibliographic record
Abstract
The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".