A unified framework for spline estimators

by Katsiaryna Schwarz
Doctoral thesis
Date of Examination:2013-01-24
Date of issue:2013-07-09
Advisor:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Martin Schlather
Referee:Prof. Dr. Robert Schaback
Referee:Prof. Dr. Andrea Krajina
Referee:Prof. Dr. Russell Luke
Referee:Prof. Dr. Preda Mihailescu
Persistent Address: http://dx.doi.org/10.53846/goediss-3930

 

 

Files in this item

Name:dissertation.pdf
Size:1.17Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

This dissertation develops a uni ed framework to study the (asymptotic) properties of all (periodic) spline based estimators, that is of regression, penalized and smoothing splines. The explicit form of the periodic Demmler-Reinsch basis of general degree in terms of exponential splines allows to derive the exact expression for the equivalent kernel of all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behavior of spline estimators, is shown to be a function of both the number of knots and the smoothing parameter. A strategy for the optimal bandwidth selection is discussed.
Keywords: B-splines; Equivalent kernels; Euler-Frobenius polynomials; Exponential splines; Demmler-Reinsch basis
 
Statistik