Optimal estimation of nonlinear functions of distribution parameters [Elektronische Ressource] / by Ana Moya

Technische Universit at DortmundDepartment of StatisticsOPTIMAL ESTIMATION OF NONLINEAR FUNCTIONSOF DISTRIBUTION PARAMETERSThesis submitted in ful llment of the requirements for the degree of Doktor derNaturwissenschaften at the Technische Universit at DortmundByAna MoyaSupervisor: Prof. Dr. TrenklerDortmund, August 2009AcknowledgementsI would like to take this opportunity to express my thanks to my thesis advisor Prof. Dr.G otz Trenkler, who guided me meticulously through the research work. Not only he guidedme on scienti c issues, but he has been also very understanding and cooperative.I also express my deepest gratitude to the \Deutsche Forschungsgemeinschaft" for nancialsupport and for providing me with an excellent and friendly working environment in theGraduiertenkolleg "Statistische Modellbildung".Special mention is also due to Eva Brune, Lars Willmes, Dr. Matthias Arnold and AntonioSucre who supported me through many important aspects of this work.I would also like to thank to my family members in Venezuela, my friends in Dortmund andcolleagues at NuTech Solutions for their great inspiration, encouragement and support, allof which I will cherish throughout my life.Finally, I thank Almighty God, for all the grace and blessing that he has showered on meto reach this stage of my academic and personal life.IIIContentsList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIIIList of Figures . . . . . . . . .