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Some Steps towards Experimental Design for Neural Network Regression

  • We discuss some first steps towards experimental design for neural network regression which, at present, is too complex to treat fully in general. We encounter two difficulties: the nonlinearity of the models together with the high parameter dimension on one hand, and the common misspecification of the models on the other hand. Regarding the first problem, we restrict our consideration to neural networks with only one and two neurons in the hidden layer and a univariate input variable. We prove some results regarding locally D-optimal designs, and present a numerical study using the concept of maximin optimal designs. In respect of the second problem, we have a look at the effects of misspecification on optimal experimental designs.

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Author:Richard Kodzo Avuglah
URN (permanent link):urn:nbn:de:hbz:386-kluedo-23493
Advisor:Jürgen Franke
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2011/06/09
Year of Publication:2011
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2011/06/07
Date of the Publication (Server):2011/06/11
Number of page:133
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):62-XX STATISTICS
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 27.05.2011