A uniform central limit theorem for neural network-based autoregressive processes with applications to change-point analysis |
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Authors: | Claudia Kirch Joseph Tadjuidje Kamgaing |
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Affiliation: | 1. Institute for Stochastics, Karlsruhe Institute of Technology (KIT), Kaiserstr. 89, 76133 Karlsruhe, Germanyclaudia.kirch@kit.edu;3. Department of Mathematics, University Kaiserslautern, Erwin-Schr?dinger-Stra?e, 67653 Kaiserslautern, Germany |
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Abstract: | We consider an autoregressive process with a nonlinear regression function that is modelled by a feedforward neural network. First, we derive a uniform central limit theorem which is useful in the context of change-point analysis. Then, we propose a test for a change in the autoregression function which – by the uniform central limit theorem – has asymptotic power one for a large class of alternatives including local alternatives not restricted to the correctly specified model. |
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Keywords: | uniform central limit theorem nonparametric regression neural network autoregressive process |
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