Nonparametric changepoint analysis for bernoulli random variables based on neural networks

  • In many medical, financial, industrial, e.t.c. applications of statistics, the model parameters may undergo changes at unknown moment of time. In this thesis, we consider change point analysis in a regression setting for dichotomous responses, i.e. they can be modeled as Bernoulli or 0-1 variables. Applications are widespread including credit scoring in financial statistics and dose-response relations in biometry. The model parameters are estimated using neural network method. We show that the parameter estimates are identifiable up to a given family of transformations and derive the consistency and asymptotic normality of the network parameter estimates using the results in Franke and Neumann Franke Neumann (2000). We use a neural network based likelihood ratio test statistic to detect a change point in a given set of data and derive the limit distribution of the estimator using the results in Gombay and Horvath (1994,1996) under the assumption that the model is properly specified. For the misspecified case, we develop a scaled test statistic for the case of one-dimensional parameter. Through simulation, we show that the sample size, change point location and the size of change influence change point detection. In this work, the maximum likelihood estimation method is used to estimate a change point when it has been detected. Through simulation, we show that change point estimation is influenced by the sample size, change point location and the size of change. We present two methods for determining the change point confidence intervals: Profile log-likelihood ratio and Percentile bootstrap methods. Through simulation, the Percentile bootstrap method is shown to be superior to profile log-likelihood ratio method.

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Metadaten
Verfasserangaben:Anthony Waititu Gichuhi
URN (Permalink):urn:nbn:de:hbz:386-kluedo-22720
Betreuer:Thomas Markwig
Dokumentart:Dissertation
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2008
Jahr der Veröffentlichung:2008
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:06.10.2008
Datum der Publikation (Server):16.10.2008
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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