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Fitting jump models. (English) Zbl 1406.93315

Summary: We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determines the shape of the resulting jump model.

MSC:

93E10 Estimation and detection in stochastic control theory
93E03 Stochastic systems in control theory (general)
60J75 Jump processes (MSC2010)
62P30 Applications of statistics in engineering and industry; control charts
93-04 Software, source code, etc. for problems pertaining to systems and control theory
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