On Nonparametric Estimators of the Density of a \nNon-negative Function of Observations
Bibliographic record
Abstract
Let {X 1 , ..., X n } be a random sample from a continuous distribution F defined on the k-dimensional Euclidean space R k , for some k ≥ 1.In many statistical applications we are interested in statistical properties of a function h(X 1 , ..., X m ) of m ≥ 1 observations.Frees (1994, J. Amer.Stat.Assoc.)considered estimating the density function g associated with the distribution functionusing the kernel method.In many applications, though, the functions of interest are non-negative where the usual symmetric kernels applied in the kernel density estimation are not appropriate.This paper adapts the alternative density estimator developed in Chaubey and Sen (1996, Statistics and Decisions) by smoothing the so called empirical kernel distribution function:where 1(A) denotes the indicator of A anddenotes sum over all possible ( n m ) combinations.Applications and asymptotic properties of the alternative estimator are investigated.
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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 | 0.032 | 0.189 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".