Time series and state space model with generalized \nextreme value distributed marginals and α-stable \ndistributed errors
Bibliographic record
Abstract
This thesis is mainly focused on the estimation and filtering of extreme events time \nseries and models with generalized extreme value distributed marginals and the multiplicative \nerrors from α-stable distribution. \nFirst a non-linear time series with Fréchet distributed marginals and α-stable \ndistributed errors is considered. To estimate the stability parameter, three recursive \nprocedures are proposed. The first is based on the Hill estimation, the second is a \nmodified Fan’s estimation that uses the property of the α-stable distribution, and the \nlast is an application of Kantorovich-Wasserstain metric. \nFor the state space model with generalized extreme value distributed marginals \nand α-stable distributed errors, the estimation is more complex, especially when the \nstability parameters are small. In the model with Gumbel distributed marginals, if \none of the stability parameter is known, a procedure that generates an ensemble from \nthe known error distribution by Monte Carlo followed by estimation is proposed. For \na model with generalized extreme value distributed marginals and unknown stability \nparameters, first a recursive regression estimation is applied to obtain the generalized \nextreme valued parameters, then the Yule-Walker estimation or generalized least \nsquare regression model is used to estimate the stability parameters. \nRegarding filtering, the estimation of unobserved states and their empirical conditional \ndensities are our interests. The estimation of states is obtained numerically \nvia Monte Carlo, based on the model structure. This procedure outperforms Kalman \nfilter. As to the empirical conditional density, sequential importance sampling with \ndifferent importance functions, particle filter with discrete sample space, auxiliary \nparticle filter and plain linearization are used and compared. \nThe asymptotic properties and rates of convergence of the proposed estimations are \nstudied analytically and through simulation. The methods and procedures developed \nin this thesis have been applied to analyze the air pollution data in New York city.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".