Autoregressive models for maxima and their applications to CH<sub>4</sub>and N<sub>2</sub>O
Bibliographic record
Abstract
Abstract Recordings of daily, weekly, or yearly maxima in environmental time series are classically fitted by the generalized extreme value (GEV) distribution that originates from the well‐established extreme value theory (EVT). One special case of such GEV distribution is the Gumbel family which corresponds to the modeling of maxima stemming from light‐tailed distributions. To capture temporal dependencies, linear autoregressive (AR) processes offer a simple and elegant framework. Our objective is to extend linear AR models in such a way that they handle Gumbel distributed maxima. To reach this goal, we take advantage of the stability of Gumbel random variables when added to the logarithm of a positive α‐stable random variable. This allows us to propose a linear Gumbel distributed AR model whose main theoretical properties are derived. For the atmospheric scientist, this link between linear AR processes and EVT widens the statistical treatment of extreme environmental recordings in which temporal dependencies are present. For example, our model is fitted to daily and weekly maxima of methane (CH4) and daily maxima of nitrous oxide (N2O) measured in Gif‐sur‐Yvette (France). Simulation results are also presented in order to assess the quality of our parameter estimations for finite samples. Copyright © 2009 John Wiley & Sons, Ltd.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".