Bootstrap Approach for Estimating Seemingly Unrelated Regressions with Varying Degrees of Autocorrelated Disturbances
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Bibliographic record
Abstract
The Seemingly Unrelated Regressions (SUR) model proposed in 1962 by Arnold Zellner has gained a wide acceptability and its practical use is enormous. In this research, two methods of estimation techniques were examined in the presence of varying degrees of first order Autoregressive [AR(1)] coefficients in the error terms of the model. Data was simulated using bootstrapping approach for sample sizes of 20, 50, 100, 500 and 1000. Performances of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators were examined under a definite form of the variance-covariance matrix used for estimation in all the sample sizes considered. The results revealed that the GLS estimator was efficient both in small and large sample sizes. Comparative performances of the estimators were studied with 0.3 and 0.5 as assumed coefficients of AR(1) in the first and second regressions and these coefficients were further interchanged for each regression equation, it was deduced that standard errors of the parameters decreased with increase in the coefficients of AR(1) for both estimators with the SUR estimator performing better as sample size increased. Examining the performances of the SUR estimator with varying degrees of AR(1) using Mean Square Error (MSE), the SUR estimator performed better with autocorrelation coefficient of 0.3 than that of 0.5 in both regression equations with best MSE obtained to be 0.8185 using $\rho = 0.3$ in the second regression equation for sample size of 50.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it