Adaptive linear estimators, using biased cramer-RAO bound
Bibliographic record
Abstract
In this paper, the biased Cramer-Rao lower bound (BCRLB) is used to derive the estimate of unknown parameters in a linear model with an arbitrary known additive noise probability density function (PDF).We show that the derived linear estimators (not unique) are linear functions of the observations. Examples are included to illustrate their performances. We show that a biased estimator obtained by optimization of BCRLB is not necessary satisfactory in a general case; therefore, additional considerations must be taken into account. If the Fisher information matrix (FIM) is singular, we use the method of singular value decomposition (SVD) to extract the parameter estimate of linear model. For example we show that in a linear model, parameter estimation based on single observation leads to the normalized least mean square (NLMS) algorithm. In this example using BCRLB optimization, we find the relation between the step size of the NLMS algorithm and bound of bias gradient matrix
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.001 | 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".