PhD Defense: Niels Aske Lundtorp Olsen

Statistical analysis of functional data with multivariate domain and response

Abstract:
Functional data analysis (FDA) is characterised by relatively small sample sizes, many observations per curve, and an issue about misaligned data. In this thesis we develop new methods and models for functional data. The focus is on multivariate responses, misalignment and local inference, three challenging fields within functional data analysis.

In the first paper of the thesis we consider a new model for multivariate, misaligned functional data. We develop low-parametric warp and cross-correlation models, and we apply the model to three different data sets. We also use of the last data set in a classification study, where we compare our model to a number of state-of-the-art methods.

The second paper of the thesis is about the same topic, but with a very different approach. By a clever parametrisation using the Cholesky decomposition, we develop a model framework that potentially allows for very fast computations.

The third paper of the thesis is about local inference for functional data. We develop a functional analogue to the Benjamini-Hochberg method as a way to deal with the multiple comparisons problem. The paper contains theoretical results about control of false discovery rates, two simulation studies and an application to satellite measurements of Earth temperatures.

The last paper of the thesis contains a statistical study of conidial discharge, where we extend the model from the first article in the context of generalised linear models. In the application we study the intensity of conidial discharge as function of time, for mycelia stored at three different temperatures.

Supervisor: Ass.Prof. Bo Markussen, MATH, University of Copenhagen

Assessment Committee

Prof. (Chairman), Helle Sørensen, University of Copenhagen

Prof. Robert Todd Ogden, Columbia University (USA)

Ass. Prof, Ana-Maria Staicu, North Carolina State University (USA