Confidence bands in quantile regression and generalized dynamic semiparametric factor models [Elektronische Ressource] / Song Song. Gutachter: Wolfgang Karl Härdle ; Ya’acov Ritov

Confidence Bands in Quantile Regression andGeneralized Dynamic Semiparametric Factor ModelsDISSERTATIONzur Erlangung des akademischen GradesDoctorateim Fach Statistics and Econometricseingereicht an derWirtschaftswissenschaftlichen FakultätHumboldt-Universität zu BerlinvonMsc. Song Song18.07.1984Präsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Wirtschaftswissenschaftlichen Fakultät:Prof. Oliver Günther, Ph.D.Gutachter:1. Prof. Dr. Wolfgang Karl Härdle2. Prof. Dr. Ya’acov Ritoveingereicht am: 07.06.2010Tag der mündlichen Prüfung: 02.08.2010The topic this thesis deals with is complex, but very interesting. I want to thank mysupervisor Prof. Dr. Wolfgang Karl Härdle and Prof. Dr. Ya’acov Ritov for the greatopportunities to learn from them and the support during the production of this thesis.To overcome all of the theoretical and empirical challenges, I also want to thank Dr. T.Vogel, Peter Bickel for their great presence.AbstractIn many applications it is necessary to know the stochastic fluctuation of the max-imal deviations of the nonparametric quantile estimates, e.g. for various parametricmodels check. Uniform confidence bands are therefore constructed for nonpara-metric quantile estimates of regression functions. The first method is based onthe strong approximations of the empirical process and extreme value theory. Thestrong uniform consistency rate is also established under general conditions.