B-SPLINE ESTIMATION FOR PARTIALLY LINEAR REGRESSION MODELS WITH HETEROSCEDASTICITY
Why this work is in the frame
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Bibliographic record
Abstract
For partially linear regression model with heteroscedastic error variances yij = x'ijβ+ g(tij) + eij, i = 1,2,…,k, j = 1,2,…,ni, and sum from i=1 to k=n where yij's are responses, β= (β,…,βP)' is an unknown parameter vector, g(.) is an unknown function over R, Xij = (xij,…,XijP)' and tij ∈[0,1] are known and nonrandom design points, and eij's are independent errors with mean 0 and variance σi2 which may be different. Based on the nonparametric component g(.) approximated by a B-spline series, a semiparametric generalized least squares estimator (SGLSE) of the parametric component βis constructed. The asymptotic distribution is established under some moment conditions on the error distributions. Most of the error distributions encountered in practice satisfy these moment conditions. A consistent estimator of the asymptotic covariance matrix is also given. Moreover, the B-spline estimation of the nonparametric component is also considered. The large sample properties of these estimators are derived for increasing k, assuming the numbers ni in the groups from a fixed sequence. Based on these asymptotic results asymptotically valid the test statistics and confidence intervals for parametric component and nonparametric component can be constructed.
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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 | 0.003 |
| 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