Optimal Designs for Minimizing Variances of Parameter Estimates in Linear Regression Models
Bibliographic record
Abstract
In statistical inference, it is important to estimate the parameters of a regression model in such a way that the variances of the estimates are as small as possible. Motivated by this fact, we have tried to address this important problem using optimal design theory. We start with some optimal design theory and determine the optimality conditions in terms of a directional derivative. We construct the optimal designs for minimizing variances of the parameter estimates in two ways. The first one is the analytic approach, in which we derive the derivatives of our criterion and solve the resulting equations. In another approach, we construct the designs using a class of algorithms. We also construct designs for minimizing the total variance of some parameter estimates. This is motivated by a practical problem in Chemistry. We attempt to improve the convergence of the algorithm by using the properties of the directional derivatives.
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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 | 0.028 | 0.074 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| 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".