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Extreme value analysis of optimal level‐crossing prediction for linear Gaussian processes
Author(s) -
Martin Rodney A.
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00791.x
Subject(s) - metric (unit) , level crossing , mathematics , event (particle physics) , limiting , kalman filter , algorithm , computer science , statistics , mathematical optimization , engineering , mechanical engineering , operations management , physics , quantum mechanics
A novel approach of combining the practical appeal of Kalman filtering with the design of an optimal alarm system for the prediction of level‐crossing events was introduced in earlier work. Here, the aim is to perform a more detailed extreme value analysis using the critical threshold that enables definition of the level‐crossing event. It will be rigorously proven that the approximations and baseline methods previously used yield important intuitive conclusions about the impact of low measurement noise and high levels on improved capability of level‐crossing predictors. Where possible, elegant closed‐form solutions for a well‐known alarm system metric in face of those limiting considerations are also provided.