Improved Nonparametric Inference for the Mean of a Bounded Random Variable with Application to Poverty Measures
Bibliographic record
Abstract
We provide new finite sample nonparametric inference methods for the mean of a bounded random variable. For this purpose, we prove that the impossibility theorem of Bahadur and Savage (1956) does not apply in this case. Next, we observe that confidence intervals for the mean of a bounded random variable can actually be derived by projection from confidence intervals for the adequate distribution function and investigate finite sample nonparametric methods based on improved Kolmogorov Smirnov statistics and likelihood ratio improvement. Further, we apply all studied inference methods on the Foster, Greer and Thorbecke (FGT, 1984) poverty measures. We show that FGT poverty measures are actually expectations of some bounded random variables, namely a mixing between a continuous bounded random variable and a mass at the poverty line. So, all inference methods for the mean of bounded random variable apply to this case. We study the relative performance of such methods. Monte Carlo simulations demonstrate the necessity of using finite sample nonparametric approaches. The asymptotic and bootstrap inference methods appear not reliable in finite sample. On the contrary, the finite sample nonparametric inference methods we propose are robust to the framework and the sample size we use. Confidence intervals we get have a very good coverage probability (always close to 100%) and a good precision. In addition, we provide explicit expressions which make them very easy to compute.
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How this classification was reachedexpand
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".