TY - BOOK

T1 - Statistical analysis of functional data

T2 - multivariate responses, misaligned data and local inference

AU - Olsen, Niels Aske Lundtorp

PY - 2018

Y1 - 2018

N2 - Functional data analysis 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 analysis (FDA). 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 classicfiation 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.

AB - Functional data analysis 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 analysis (FDA). 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 classicfiation 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.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122255729105763

M3 - Ph.D. thesis

BT - Statistical analysis of functional data

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -