Estimation of a regression function by maxima of minima of linear functions [Elektronische Ressource] / vorgelegt von Conny Clausen

——————————————————–Estimation of a Regression Functionby Maxima of Minima of LinearFunctions———————Dissertationzur Erlangung des Gradesdes Doktors der Naturwissenschaftender Naturwissenschaftlich-Technischen Fakult¨atender Universit¨at des Saarlandesvorgelegt vonConny Clausen—————————————————————————Saarbru¨cken 2008Tag des Kolloquiums: 13.06.2008Dekan: Prof. Dr. Joachim WeickertPru¨fungsausschuss: VorsitzenderProf. Dr. J¨org EschmeierBerichterstatterProf. Dr. Michael KohlerProf. Dr. Alfred K. LouisAkademischer MitarbeiterDr. Christoph BarbianTomy parentsAbstractThe estimation of a multivariate regression function from independentand identically distributed random variables is considered. First wepropose and analyse estimates which are defined by minimisation ofthe empirical L risk over a class of functions consisting of maxima of2minima of linear functions. It is shown that the estimates are stronglyuniversally consistent. Moreover results concerning the rate of con-vergence of the estimates with data-dependent parameter choice using‘splitting the sample’ are derived in the case of an unbounded responsevariable. In particular it is shown that, for smooth regressionfunctionssatisfying the assumptions of single index models, the estimate is ableto achieve (up to some logarithmic factor) the corresponding optimalone–dimesional rate of convergence.