Testing the heteroscedastic error structure in quantile varying coefficient models
Bibliographic record
Abstract
Abstract In mean regression the characteristic of interest is the conditional mean of the response given the covariates. In quantile regression the aim is to estimate any quantile of the conditional distribution function. For given covariates, the conditional quantile function fully characterizes the entire conditional distribution function, in contrast to the mean which is just one of its characteristic quantities. Regression quantiles substantially out‐perform the least‐squares estimator for a wide class of non‐Gaussian error distributions. In this article we consider quantile varying coefficient models (VCMs) that are an extension of classical quantile linear regression models, in which one allows the coefficients to depend on other variables. We consider VCMs with various structures for the variance of the errors (the variability function) in order to allow for heteroscedasticity. For longitudinal data, the time (T) dependent coefficient functions in the signal and the variability functions are estimated with P‐splines (Penalized B‐splines). Consistency of the proposed estimators is proved. Further, likelihood‐ratio‐type tests are considered for comparing the variability functions. The performance of the testing procedure is illustrated on simulated and real data.The Canadian Journal of Statistics46: 246–264; 2018 © 2017 Statistical Society of Canada
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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 | 0.046 | 0.198 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".