General adapted‐threshold monitoring in discrete environments and rules for imbalanced classes

Ansgar Steland, Ewaryst Rafajłowicz and Wojciech Rafajłowicz

Statistica Neerlandica, 2025, vol. 79, issue 1

Abstract: Having in mind applications in statistics and machine learning such as individualized care monitoring, or watermark detection in large language models, we consider the following general setting: When monitoring a sequence of observations, Xt, there may be additional information, Zt, on the environment which should be used to design the monitoring procedure. This additional information can be incorporated by applying threshold functions c(Zt) to the standardized measurements to adapt the detector to the environment. For the case of categorical data encoding of discrete‐valued environmental information we study several classes of level α threshold functions including a proportional one which favors rare events among imbalanced classes. For the latter rule asymptotic theory is developed for independent and identically distributed and dependent learning samples including data from new discrete autoregressive moving average model (NDARMA) series and Hidden Markov Models. Further, we propose two‐stage designs which allow to distribute in a controlled way the α budget over an a priori partition of the sample space of Zt. The approach is illustrated by a real medical data set.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/stan.12352

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:stanee:v:79:y:2025:i:1:n:e12352

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0039-0402

Access Statistics for this article

Statistica Neerlandica is currently edited by Miroslav Ristic, Marijtje van Duijn and Nan van Geloven

More articles in Statistica Neerlandica from Netherlands Society for Statistics and Operations Research
Bibliographic data for series maintained by Wiley Content Delivery ().