Bibliographic record
Abstract
This paper extends a result of Godambe on parametric estimation for discrete time stochastic processes to nonparametric estimation for the continuous time case. Following Hasminskii and Ibragimov (1980), the nonparametric problem is formulated as a parametric one but with infinite dimensional parameter. Let { P} be a family of probability measures such that (D,F,P) is complete, (Ft,t~O) is a standard filtration, and X=(XI,FI,t~O) is a semimartingale for every P £ { P}. For a parameter O'(t) suppose Xl=V, 0+ Aft 0 where the Vo process is predictable and locally of bounded variation and the H ~ proc~ss is a local martingale. Consider estimating equations for O'(t) of the form t Jau,adMu,o=O where the ao- process is predictable. Under regularity conditions, an o optimal form for a o in the sense of Godambe (Ann. Math. Statist. 31 (1960), 1208-11) is determined. The method is applied to cases where M is linear in 0'. It is shown that Nelson-Aalen estimate for the cumulative hazard function is optimal in Godambe's sense. A new estimate is obtained for an extended gamma process model. Semimartingale theory is used to indicate proofs of asymptotic normality of test statistics under the null hypotheses considered.
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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 | 0.001 | 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) | 0.024 | 0.003 |
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; both teacher heads agree on what is shown here.
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".