Robust changepoint detection in the variability of multivariate functional data
Bibliographic record
Abstract
We consider the problem of robustly detecting changepoints in the variability of a sequence of independent multivariate functions. We develop a novel changepoint procedure, called the functional Kruskal–Wallis for covariance changepoint procedure, based on rank statistics and multivariate functional data depth. The functional Kruskal–Wallis for covariance changepoint procedure allows the user to test for at most one changepoint or an epidemic period, or to estimate the number and locations of an unknown number of changepoints in the data. We show that when the ‘signal-to-noise’ ratio is bounded below, the changepoint estimates produced by the functional Kruskal–Wallis for covariance changepoint procedure attain the minimax localisation rate for detecting general changes in distribution in the univariate setting. We also provide the behaviour of the proposed test statistics for the at-most-one-change and epidemic settings under the null hypothesis and, as a simple consequence of our main result, these tests are consistent. In simulation, we show that our method is particularly robust when compared to similar changepoint methods. We present an application of the functional Kruskal–Wallis for covariance changepoint procedure to intraday asset returns and functional magnetic resonance imaging scans. As a by-product of our main result, we provide a concentration result for integrated functional depth functions, which may be of general interest.
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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 | 0.012 | 0.074 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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".