Local Smoothing Methods with Regularization in Nonparametric Regression Models [Elektronische Ressource] / Mohammad Fawaz Kourabi. Betreuer: Jürgen Franke
116 Pages
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Local Smoothing Methods with Regularization in Nonparametric Regression Models [Elektronische Ressource] / Mohammad Fawaz Kourabi. Betreuer: Jürgen Franke

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Local Smoothing Methods with Regulariza-tion in Nonparametric Regression ModelsMohammad Fawaz KourabiLOCAL SMOOTHING METHODS WITHREGULARIZATION IN NONPARAMETRICREGRESSION MODELSMohammad Fawaz KourabiVom Fachbereich Mathematikder Technischen Universit¨at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Jurgen¨ Franke2. Gutachter: Prof. Dr. Klaus RitterDatum der Disputation: 15. August 2011D 386To my parents, and SawsaniiTable of ContentsTable of Contents iiiAbstract vAcknowledgements vi1 Preliminaries 11.1 Preliminary notations and definitions . . . . . . . . . . . . . . . . . . 11.2 Building the normed vector space of Matrices . . . . . . . . . . . . . 42 Estimation and smoothing 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Local-average methods, basic idea of smoothing . . . . . . . . . . . . 92.3 Kernel methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Bandwidth selection . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 Leave-one-out cross-validation method . . . . . . . . . . . . . 192.4 Spline Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Approach by Mr´azek et al. . . . . . . . . . . . . . . . . . . . . . . . . 232.5.1 Some Special Cases . . . . . . . . . . . . . . . . . . . . . . . .

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Published 01 January 2011
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