Partial Least Squares for Serially Dependent Data

by Marco Singer
Doctoral thesis
Date of Examination:2016-08-04
Date of issue:2016-09-12
Advisor:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Axel Munk
Persistent Address: http://dx.doi.org/10.53846/goediss-5828

 

 

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Abstract

English

In the first paper we consider the partial least squares algorithm for dependent data and study the consequences of ignoring the dependence both theoretically and numerically. Ignoring nonstationary dependence structures can lead to inconsistent estimation, but a simple modification leads to consistent estimation. A protein dynamics example illustrates the superior predictive power of the method. For the second paper we consider the kernel partial least squares algorithm for the solution of nonparametric regression problems when the data exhibit dependence in their observations in the form of stationary time series. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are established under a source condition. The impact of long range dependence in the data is studied both theoretically and in simulations.
Keywords: Dependent data, Kernel partial least squares, Latent variable model, Long range dependence, Nonparametric regression, Nonstationary process, Partial least squares, Protein dynamics, Source condition, Stationary process
 
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