A comparative study of some existing post-model-selection inferential methods in linear regression models
Bibliographic record
Abstract
It is widely recognized that disregarding the uncertainty rooted in data-dependent model selection procedures invalidates various uncertainty measurements which were used to be justified by classical statistical theories. Categorized according to different types of post-selection estimation targets, there has been a great amount of new insights proposed to provide valid post-selection inference for both population- and projection-based regression coefficients. In this thesis, we first motivate the study of post-selection inference through two simulated examples. Upon acknowledging the necessity for valid inference after model selection, we then perform a thorough literature review of major landmarks in tracking the post-selection sampling distribution of regression parameter estimates and coverage properties of naive confidence intervals/regions. This is followed by a selective overview of existing prominent post-selection statistical inferential paradigms for both population- and projection-based targets. Particularly, emphasis is placed on the construction of valid post-selection confidence intervals. Focusing on methods designed for the projection-based regression coefficients, we carry out simulation studies to compare the performance of various post-selection confidence intervals constructed by these methods. Under the presumed framework of linear regression model with i.i.d. Gaussian errors, this simulated comparison contributes quantitatively to the understanding of merits and limitations of various post-selection confidence intervals for projection-based regression coefficients in terms of average conditional coverage probability, average length of confidence intervals and symmetry of coverage hits and misses.
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How this classification was reachedexpand
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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".