Consistency of modified LS estimation method for identifying 2-D noncausal SAR model parameters
Bibliographic record
Abstract
There are two main methods for estimating the parameters of two-dimensional (2-D) noncausal simultaneous autoregressive (SAR) models. One is the least-squares (LS) and the other is the maximum likelihood (ML). The asymptotically unbiased and consistent ML, method is computationally unattractive even after some approximations have been introduced. On the other hand, the computationally efficient conventional LS method does not produce accurate parameter estimates in this case due to the noncausality of the models. In order to improve the estimation accuracy and keep the computational efficiency of the LS method, an unbiased modified LS estimator was recently proposed. However, a very important matter remains to be addressed. As of yet, a mathematical proof for the consistency of the modified LS estimator has not been presented anywhere in the literature. The results of previous computer simulation studies on this estimator have been based on only data sample windows of fixed sizes. The studies are limited by the fact that the variances and mean square errors of the parameter estimates as functions of the data window sizes could not be deduced from the results. Therefore, the results presented to date cannot be used to demonstrate either the consistency or the convergence properties of the estimator. Based on both analytical and experimental investigations, this paper proves the consistency of the modified LS estimator. A detailed theoretical analysis and a new numerical example are included in the paper. The experimental results corroborate the theoretical results.>
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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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".