Performance Comparison of Three Ratio Estimators of the Population Ratio in Simple Random Sampling Without Replacement
Bibliographic record
Abstract
This study aims to compare the efficacy of three ratio estimators for estimating the population ratio in simple random sampling without replacement (SRSWOR). The estimators under consideration are a customary ratio estimator (~R1), a ratio estimator based on a transformed mean estimator (~R2) introduced by Onyeka et al. [1], and a regression-type estimator (~R3) proposed by Onyeka et al. [2]. We assess the performance of these estimators across three distributions (bivariate normal, bivariate Poisson log-normal, and bivariate Cauchy) while varying both correlation coefficients and sample sizes, utilizing Mean Square Error (MSE) and Percent Relative Efficiency (PRE) as evaluation criteria. The results indicate that for a bivariate normal distribution, the ~R1 and ~R2 estimators consistently outperformed the ~R3 estimator across all sample sizes and correlation coefficients. The ~R2 estimator demonstrated superiority with very small sample sizes, while ~R1 exhibited better performance in small sample sizes. The ~R2 estimator remained reliable for moderately sized samples, demonstrating consistent efficiency. In large samples, ~R2 maintained its performance advantage, except in weak correlation coefficients, where ~R1 proved superior. For a bivariate Poisson lognormal distribution, both ~R2 and ~R3 performed significantly better than ~R1 for very small sample sizes, irrespective of correlation direction and strength. For moderately sized samples, ~R2 and ~R3 consistently excelled, with ~R2 leading in cases with positive correlation coefficients. For large sample sizes with negative correlation coefficients, both ~R2 and ~R3 were comparable effective and significantly better than ~R1. Conversely, with positive correlation coefficients, the ~R1 estimator significantly outperformed both ~R2 and ~R3. In a bivariate Cauchy distribution, the ~R1 estimator demonstrated notable and consistent superiority over the ~R2 and ~R3 estimators across all sample sizes and correlation coefficients.
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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 | 0.046 | 0.182 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".