Robust estimation of the sample mean variance for Gaussian processes with long-range dependence
Bibliographic record
Abstract
We introduce a method to robustly estimate the variance of the sample mean for two Gaussian processes exhibiting Long-Range Dependence (LRD): fractional Gaussian noise, fGn(H), and fractional autoregressive integrated moving average, FARIMA(0, H, 0) processes. Our method is based on a combination of two estimators of H which are functions of a multitaper estimator of the log spectral density: a robust estimator which uses a limited number of frequencies near the origin, and an estimator which uses (almost) all of the frequencies. An important feature of our method is a test to differentiate between fGn(H) and FARIMA(0, H, 0) which, under a correct decision, allows us to estimate the Hurst parameter H using the correct model specification. Differentiating between fGn(H) and FARIMA(0, H, 0) with Gaussian innovations is important to estimate the sample mean variance and for statistical inference about the process location parameter. Numerical comparisons are made against existing estimators including parametric and semi-parametric methods in Fourier frequency and wavelet domains.
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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 | 0.000 | 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".