Optimal estimating functions in incomplete data and length biased sampling data problems
Bibliographic record
Abstract
Abstract It is well known that the score function is the optimal estimating function among all regular unbiased estimating functions (Godambe, 1960). In the presence of incomplete data such as missing data or length biased sampling data, Horvitz and Thompson's (1952) method is an effective way of eliminating the possible bias induced by using complete data only. In this article, we show that the inverse weighted Horvitz and Thompson score estimating function is not optimal in the presence of incomplete data. By using Godambe's estimating function theory, we can identify the optimal estimating function in this situation. In the case of the accelerated failure time model with length bias sampling data, the optimal estimating function can produce an unbiased estimator for the slope parameter even when the underlying density function is misspecified. Simulation studies show that the estimate derived from the optimal estimating function can be substantially better than the estimate derived from the inverse weighted score estimating function. The Canadian Journal of Statistics 39: 510–518; 2011 © 2011 Statistical Society of Canada
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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 | 0.071 | 0.216 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| 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".