Efficient and robust estimation of tail parameters for Pareto and exponential models
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, a new efficient and robust estimator of the Pareto tail index is proposed. Although the emphasis is on the Pareto distribution, all results are valid for the estimation of the scale/rate parameter of the two-parameter exponential distribution. The approach is to assume that the observations were generated from the FLLP-contaminated Pareto, that is, a mixture of the Pareto and FLLP distributions. The latter is an original distribution designed specifically to represent any outlier distribution. The parameters are estimated using an iterative process adapted from the expectation-maximization (EM) algorithm to optimize the properties of the estimators in a robustness context. A robust confidence interval for the Pareto tail index is also given. It is shown through different asymptotic results that these estimators reach a breakdown point of 50% with full efficiency. Their simultaneous high efficiency and high robustness are also shown for finite samples in a large Monte Carlo simulation study. Finally, an example with a real dataset of daily crude oil returns is given.
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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 | 0.002 |
| 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