Testing for change in the mean via convergence in distribution of sup-functionals of weighted tied-down partial sums processes
Bibliographic record
Abstract
Let X 1,..., X n, n > 1, be nondegenerate independent chronologically ordered realvalued observables with finite means. Consider the “no-change in the mean” null hypothesis H 0: X 1,..., X n is a randomsample on X with Var X <∞. We revisit the problem of nonparametric testing for H 0 versus the “at most one change (AMOC) in the mean” alternative hypothesis H A: there is an integer k*, 1 ≤ k* < n, such that EX 1 = · · · = EXk* ≠ EXk*+1 = ··· = EX n. A natural way of testing for H 0 versus H A is via comparing the sample mean of the first k observables to the sample mean of the last n - k observables, for all possible times k of AMOC in the mean, 1 ≤ k < n. In particular, a number of such tests in the literature are based on test statistics that are maximums in k of the appropriately individually normalized absolute deviations Δk = |S k/k - (S n - S k)/(n - k)|, where S k:= X 1 + ··· + X k. Asymptotic distributions of these test statistics under H 0 as n → ∞ are obtained via establishing convergence in distribution of supfunctionals of respectively weighted |Z n(t)|, where {Z n(t), 0 ≤ t ≤ 1}n≥1 are the tied-down partial sums processes such that $${Z_n}\left( t \right): = \left( {{S_{\left\lceil {\left( {n + 1} \right)t} \right\rceil }} - \left[ {\left( {n + 1} \right)t} \right]{S_n}/n} \right)/\sqrt n $$ if 0 ≤ t < 1, and Z n(t):= 0 if t = 1. In the present paper, we propose an alternative route to nonparametric testing for H 0 versus H A via sup-functionals of appropriately weighted |Z n(t)|. Simply considering max1ɤk 2. We believe the weight function t(1 - t) for sup-functionals of |Z n(t)| has not been considered before.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.041 | 0.205 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| 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".