The Naive Estimator of a Poisson Regression Model with a Measurement Error
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Bibliographic record
Abstract
We generalize the naive estimator of a Poisson regression model with a measurement error as discussed in Kukush et al. in 2004. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the explanatory variable and measurement error are not limited to a normal distribution. We clarify the requirements for the existence of the naive estimator and derive its asymptotic bias and asymptotic mean squared error (MSE). The requirements for the existence of the naive estimator can be expressed using an implicit function, which the requirements can be deduced by the characteristic of the Poisson regression models. In addition, using the implicit function obtained from the system of equations of the Poisson regression models, we propose a consistent estimator of the true parameter by correcting the bias of the naive estimator. As illustrative examples, we present simulation studies that compare the performance of the naive estimator and new estimator for a Gamma explanatory variable with a normal error or a Gamma error.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it