Reduced Mean-Square Error Quadratic Inverse Spectrum Estimator
Bibliographic record
Abstract
A new spectrum estimator is introduced. The new estimator exploits quadratic-inverse theory to attain improved mean-square error performance over the standard multitaper spectrum estimators. The standard, non-adaptive, eigenvalue weighted multitaper estimator is obtained by averaging a high-resolution inconsistent spectrum estimator over the estimator bandwidth. The improved performance of the proposed estimator results from replacing this average with a weighted average computed in the space spanned by the quadratic-inverse basis. The weighting, determined analytically, is chosen such that the resulting estimator minimizes the sum of the variance and the square of the in-band bias; neglecting bias due to spectral leakage and potential bias due to the possible incompleteness of the quadratic-inverse basis. For a white spectrum the neglected bias is found to be as small as that of a standard, non-adaptive multitaper spectrum estimator. The relative reduction of the mean-square error of the proposed spectrum estimator is validated by simulation for an ARMA(4,2) process, and results in a typical mean-square error reduction of 5% for large time-bandwidth parameters and 20% for a time-bandwidth parameter of four, when compared to the non-adaptive, non-eigenvalue weighted multitaper estimator. When compared to the adaptive multitaper spectrum estimator, larger mean-square error improvements are attainable. An expression for the theoretical probability density function for the proposed estimator is given. It is found to be as accurate as the asymptotic probability density function for the standard multitaper estimator.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".