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Extreme value analysis of optimal level-crossing prediction for linear Gaussian processes. (English) Zbl 1281.60039

Summary: 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.

MSC:

60G25 Prediction theory (aspects of stochastic processes)
60G15 Gaussian processes
62G32 Statistics of extreme values; tail inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
93E11 Filtering in stochastic control theory

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