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A uniform central limit theorem for neural network-based autoregressive processes with applications to change-point analysis
Authors:Claudia Kirch  Joseph Tadjuidje Kamgaing
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
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.
Keywords:uniform central limit theorem  nonparametric regression  neural network  autoregressive process
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