## A uniform central limit theorem for neural network based autoregressive processes with applications to change-point analysis

• We consider an autoregressive process with a nonlinear regression function that is modeled by a feedforward neural network. We derive a uniform central limit theorem which is useful in the context of change-point analysis. 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.

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Author: Claudia Kirch, Joseph Tadjuidje Kamgaing urn:nbn:de:hbz:386-kluedo-16921 Report in Wirtschaftsmathematik (WIMA Report) (138) Preprint English 2011 2011 Technische Universität Kaiserslautern 2011/03/25 autoregressive process; neural network ; nonparametric regression ; uniform central limit theorem Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F05 Central limit and other weak theorems 62-XX STATISTICS / 62Jxx Linear inference, regression / 62J02 General nonlinear regression 62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M45 Neural nets and related approaches Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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