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.

Metadaten
Author:	Claudia Kirch, Joseph Tadjuidje Kamgaing
URN:	urn:nbn:de:hbz:386-kluedo-16921
Series (Serial Number):	Report in Wirtschaftsmathematik (WIMA Report) (138)
Document Type:	Preprint
Language of publication:	English
Year of Completion:	2011
Year of first Publication:	2011
Publishing Institution:	Technische Universität Kaiserslautern
Date of the Publication (Server):	2011/03/25
Tag:	autoregressive process; neural network; nonparametric regression; uniform central limit theorem
Faculties / Organisational entities:	Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:	5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):	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
Licence (German):	Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011