Spline Estimation of Principal Curves

Abstract

Finding low-dimensional approximations to high-dimensional data is one of the most important topics in statistics, which has also multiple applications in economics, engineering and science. One suggestion in the literature ,based on kernel smoothing, is a non-linear generalization of principal components. This kernel-based approach comes with several complications. Therefore the purpose of this thesis is to provide an alternative based on spline smoothing which produces more reliable results.