Identification and Efficient Estimation in Regression Analysis with Response Missing Not At Random
Bibliographic record
Abstract
Missing-data is a pervasive problem in regression analysis, compromising the accuracy and efficiency of parameter estimates.This paper focuses on the challenging scenario of missing not at random (MNAR) data, where the missingness of a value is linked to the value itself.Traditional approaches to addressing MNAR data confront a trade-off: imposing stringent assumptions about the missingness mechanism can enhance efficiency but curtail robustness, whereas accommodating model misspecification can bolster robustness but at the expense of efficiency.In addition, assuming a nonparametric MNAR mechanism will lead to model identifiability issues.We propose a novel approach that overcomes this limitation.Firstly, we address the model identifiability issue using the shadow variable.Then, by leveraging the sieve method, we can model the MNAR mechanism nonparametrically.This approach achieves the best of both worlds: it gains robustness by avoiding strict assumptions about the missingness mechanism while simultaneously achieving the semiparametric efficiency bound for the parameter of interest (meaning our estimator has the lowest possible Statistica Sinica: Newly accepted Paper asymptotic variance).The paper delves into the theoretical framework, outlining conditions for identifiability, constructing the semiparametric likelihood function, and rigorously proving the estimator's semiparametric efficiency.Additionally, we present an EM-type algorithm for practical implementation, discussing the E-step and M-step iterations and variance estimation methods.Finally, simulations and a real-data application demonstrate the effectiveness of our proposed method compared to existing approaches.
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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 | 0.025 | 0.085 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".