On some non parametric estimators of the quantile density function for a stationary associated process
Bibliographic record
Abstract
In this article, we consider smooth estimators for the quantile density function (qdf) for a sequence {Xn,n≥1} of stationary non negative associated random variables with a common marginal distribution function. The qdf is given by q(u)=Q′(u),u∈(0,1), Q(u) representing the corresponding quantile function. The smooth estimators of q(u) considered here are adapted from those of Q(u) considered in Chaubey, Dewan, and Li (Citation2021). A few asymptotic properties of these estimators are established parallel to those in the i.i.d. case. A numerical study comparing the mean squared errors of various estimators indicates the advantages and a few limitations of various estimators. The smoothing parameter is selected based on the BCV and RLCV (a variation of likelihood cross-validation) criteria. It is concluded, based on the numerical studies, that the RLCV criterion may produce over-smoothing, hence BCV criterion may be preferable. The numerical studies also suggest that, overall, the estimator proposed by Soni, Dewan, and Jain (Citation2012) seems to have some advantage over the other estimators considered in this article.
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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 | 0.007 | 0.046 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 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".