ASYMPTOTIC DISTRIBUTION OF THE ESTIMATED BDS STATISTIC AND RESIDUAL ANALYSIS OF AR MODELS ON THE CANADIAN LYNX DATA
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Bibliographic record
Abstract
The Brock–Dechert–Scheinkman (BDS) statistic is a nonparametric statistic based on correlation integral for testing independence. It has a special ability to identify dependence in a given time series generated by some simple dynamic systems when many conventional test statistics are not able to distinguish this type of time series from observations of independent, identically distributed (IID) random variables. Using the contiguity property derived from the local asymptotic normality for the log-likelihood ratio of nonlinear autoregressive processes, we prove the central limit theorem for the estimated BDS statistic on the residuals of fitting nonlinear autoregressive models. Comparative studies on the BDS statistic and some other nonparametric statistics on simulated time series and residuals from the AR models on the Canadian lynx are also provided in this paper.
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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 | 0.000 |
| 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